I think this is going to be a state issue. I don't know where you are located, but I would suggest contacting your State's agency that handles Boat titles, and get their guidance.
Here in Texas, an outboard motor has a separate title from the boat. The Texas Parks & Wildlife has a way to apply for a lost title. They also have a system where you can get the boat and motor title information, owner, lienholder, etc. << This is really handy.
The inboard motor is specifically listed on the title of the boat. When you put a lien on the title for a boat with an inboard motor, that lien covers the boat and the motor.
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