Just to put the facts straight (and to refute the frankly ludicrous idea that the German government would "hide" Holocaust-related material):
The International Tracing Service has answered those requests for six and a half decades. This has been the purpose of its archives from the very beginning.
The ITS and its archives go back to a tracing service founded by the International Red Cross in 1943. After the war, the Allied Forces established the ITS in Germany as a permanent institution to answer inquiries from Holocaust survivors and family members and to collect all available records about killed or missing civilians. The ITS is funded by the German government and has answered millions of tracing requests.
I don't know how the Nabokov family learned about Sergey's fate, but their source of information was probably the Red Cross tracing service or the ITS itself.
Jan