Re: Info on Leah/Luba Gertzovsky and possible son/ step son Jack Miller #belarus
If Jack MILLER was in London (you have than photo) and assuming that Jack returned to the U.S., you can search incoming passenger manifests for Jack MILLER returning from London.
Hopefully you have an approximate year that Jack sailed from London to NY (either the first time, or later if he traveled more than once.)
The biggest entry point was NY (many other ports, of course.) Here is a good place to start searching incoming passengers to NY:
You can search for Jack (or maybe Jacob?) MILLER, town name: London. You can limit the search by approximate year of birth or year range of arrival.
If you find Jack on a manifest than you'll have more info to find him on census, etc.
Good luck in your search,