Depends on specifics, but I got treatment at the NIH (in California) just over a year ago, and found I could do further treatment here -- I could actually bring the drugs (and this was a drug trial, but it still was allowed). (THis was last summer -- I wasn't really moved over here at that point, but just spending time here on extended holiday.)
I brought my records from my haem/onc when I officially moved here this summer, and sat down with my doc at the start to go through it all (just saw him today for my FBC), and so far, so good. If I require further treatment, I may even be able to have the drugs shipped here . . . the two docs would stay in contact and co-manage my treatment.
You should be okay, but nothing is 100% certain, of course. I, however, had no problems.