I know only that in 1988 I went to Dutch Embassy in Moscow and
gave a package with mine and wife's documents (Diplomas, employment
history ("trudovaya knizhka"), and something else).
We did not go to Israel, but to the US (via Austria and Italy),
and we received the package with the documents (a few things were
missing though ...) in about 6 months after coming to the US.
I am not exactly sure what agency was responsible for that, but
because we worked with HIAS, I just guess that they should know about
Bessarabia SIG Leader and Coordinator