My understanding is that NY DMV is "Guilty until proven innocent".
If you can't prove the purchase of the motor & trans, THEN it is considered not purchased (ie: stolen).
I read a story a while back on the FFR forum that someone had built a '33 Hotrod, took it for inspection, couldn't prove the purchase of the engine (don't remember about the tranny) and they would not let him take the engine home, and as long as it was in the car, it stayed TOO! He returned with a cherry picker and some tools, removed the engine and trailered the car back home. That is just ridiculous government / DMV BS.
Many DMV are a PITA. When I registered my FFR in MO last year. They temporarily mis-located an internal form (sending from one office in one city to another city) it was internal and I couldn't do anything about it, until it magically appeared weeks later! There was another form, that I filled out for vintage plates and mailed to the state capital via USPS registered mail. It arrived at the government building, THEY SIGNED FOR IT (I had a USPS confirmation), THEN THEY LOST IT
IN THE BUILDING. After almost 2 weeks of trying to find it and me calling them every day and spending hours on the phone, they declared it lost and asked me why I didn't fax it to them! I said because there was no fax info on the form and no one said I could!! I fax'd it and they issued my plates the next day. THEN 1 month later, I got a letter stating that they couldn't issue my vintage plates because the license number was already in use! They were correct, I looked it up and it was "in use" BY ME!!
Idiots
Good luck! get as much information as possible, double check everything, and make copies of every form.