The wall's arrival is just the latest, if bulkiest, purchase by Jampol, who has been collecting since he was nine years old. His first acquisition was a 1950s Berlin police uniform. Now 27, the southern Californian owns the largest collection of East German (GDR) artefacts outside Germany.
Jampol's boyish interest became the basis for his ongoing graduate studies at University of California, Los Angeles, (UCLA) and now the University of Oxford. According to Jampol, it became apparent quite quickly that 'there was a significant gap between the resources students like me needed for their work and the accessibility of material'.
His collecting took off when he inherited $300,000 from his grandfather. While his brothers bought fast cars, he bought Stasi surveillance equipment and set about gathering together one of the world's largest collections of cold war artefacts and creating a home for it.
The Wende Museum is in Culver City, best known as the former home of the MGM Studios, where Gone With the Wind was shot. It has been open for a year and comprises a suite of galleries, stores, meeting rooms and a library over two floors of a former office block.
At first glance this is an unlikely setting for a new museum cum research centre, but the Simon Wiesenthal Museum of Tolerance is nearby and this part of Los Angeles is on the up.
Jampol organises regular shipments from Berlin, where he has two full-time scouts working on his behalf. When I visited the Wende in September, the small team was getting to grips with the latest consignment - five palettes of material including fashion magazines, comics and toys all packed into banana boxes augmenting the 30,000 pieces already being sifted and documented.
Visitors are greeted by a re-creation of a Tradition Hall, a room attached to a factory that would have been used for political meetings. Its deep red walls and sombre mix of German and Russian communist paraphernalia contrast with the garish architecture of California consumer society that you've left outside.
Upstairs, the displays have been curated and interpreted by Jampol. On one wall a selection of ornamental painted plates - so many that the one given by Saddam Hussein to Erich Honecker, the former East German leader, remains in store. There is also a selection of socialist realist paintings and heroic sculpture as well as posters, with topics ranging from political propaganda to an anti-smoking campaign.
Jampol's aim is to focus on 'the recognition and understanding of the effects of the cold war culture on the inhabitants of eastern Europe'; the labels are certainly impartial. But visitors who have no specialist knowledge of the period could benefit from background information to provide a context.
In a separate room, a small temporary exhibition looks at official youth culture and the ways in which recreation was politicised; there is a World Youth Festival vase dating from 1951, which was presented to a member of the East German delegation as a reminder that the festival 'showcases the physical superiority of the socialist body'.
This display in particular reflects a move towards collecting personal material such as photo albums, school books and diaries: a way of 'penetrating the cultural life of the GDR', according to Jampol.
He is keen to emphasise that what he collects reflects the evolution of eastern European society after the second world war, not only the moment the iron curtain descended.
Behind the scenes, there is a well-organised store and a small team of researchers working to the strains of marching music. Stasi surveillance equipment, statues of Lenin (one painted green and pink during the 1989 Leipzig riots and found in the rubble of discarded busts and sculpture outside the city), Olympic uniforms from the 1970s, postal service uniforms, army uniforms… the collection is certainly eclectic. Volunteer archivists are working through entire runs of newspapers, periodicals, books and private papers.
Jampol appears to have collected anything he could lay his hands on to start with, so the quality varies. Among his personal 'star items' is a model of Checkpoint Charlie with original Stasi marks noting which spy operated where.
Although the museum is only open by appointment, there are occasional open house days and movie nights, which have helped establish good relationships with local audiences. The Wende has established tentative links with organisations such as the Goethe Institute in LA, which donated bookshelves for the store; UCLA interns work on the archives.
The museum used the imminent arrival of a piece of the Berlin Wall to set up an imaginative outreach project with high schools and summer camps.
Kelly Ann Kolar, the curator of the Wende, took large, blank pieces of wall to groups such as Camp Good in the Hood, which encourages inner-city kids to express ideas about their communities and politics. The result is graphic work relating to gangs, drugs and the pressure to be beautiful.
Los Angeles has long provided a home to central and eastern Europeans émigrés. Billy Wilder, Bertold Brecht and Thomas Mann fled Nazi Germany to California, while Max Factor packed up his make-up box before the Bolsheviks seized power.
Recent immigrants include a large Russian émigré community. The Wende team is planning an oral history project to record the memories of those who lived behind the iron curtain.
Jampol's funding of the museum is supplemented by grants. In 2004, the London-based Lisbet Rausing Charitable Fund gave £1m towards acquisitions and administration. So impressed were the trustees with progress in the first year that they granted a further £600,000 over five years to fund an archivist post and a collections management database.
But according to the German newspaper Der Spiegel, Jampol - and the museum - is not without his detractors. A tussle over the domain name 'cold war museum' led to a legal case. He has also been criticised by museums in Leipzig, Bonn and Berlin.
The GDR historian Rainer Eckert has gone so far as to claim that 'almost everything is already documented in Germany. There are huge collections. I don't really see what this could add to the debate'.
Jampol remains excited about his work and relishes the fact that the organisation and the Wende Museum are, at this stage, relatively small. He has brought together archivists and museum professionals who complement his own academic background and who are developing a strategy for the museum.
This will move it away from simply rescuing material to making the collection accessible via a website, and lending more to organisations such as the Imperial War Museum and the RAF Museum in Cosford, which is opening a large cold war exhibition at the end of next year.
Jampol says that there is still a lot to do at the Wende. Well into a PhD in modern history at Oxford, Jampol commutes between the UK, LA and Berlin. I caught up with him in Berlin, where he was completing the purchase of a base at an East German army camp, to expand the German operation.
Where five years ago, there had been no support for his work in Germany, for Jampol the 'time is right' to focus on Berlin. While keen to emphasise that the Wende Museum collection is not about exploring military history, he is attracted by the impressive backdrop that the base would give to a permanent exhibition in the city.
But Jampol is astute enough to realise that being taken seriously will be critical to his success in America and Germany. He takes advice from the international museum community and is gifting a second segment of the wall to the City of Los Angeles, which is twinned with Berlin.
There are even plans to generate touring exhibitions to spread the message about the museum. Jampol's sincerity cannot be doubted, nor his commitment to collecting and studying a period in history that has obsessed him since childhood.
Caroline Worthington is the curator of art at York Museums Trust