Did you make a report? If not you'll have to make the points to get an ID such as passport, proof of address, social security. License the best is to get it from California and then make the change to NY otherwise you will have to start the process all over such as taking the tests including road test. Also you should go to the NYS DMV open the portal and look for the information related to lost license and changing license from another state. My best to you.
Sorry I can't speak on that Issue I don't know about that.
Most likely yes they will good luck
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