Ask him why he has no motivation. Talk to him. I wonder...is he simply overqualified for the job, or feel it's beneath him? Maybe he feels he should make more money? Maybe he's been there forever and simply has grown bored. Find out why.
One poster above mentioned giving written warnings/incident reports. I'd be willing to bebet that you humiliate him a few times by giving him those warnings and he will be leaving on his own. Is that a bad thing? At worst, as mentioned, you now have a paper trail on him. When's his next performance review? Don't go easy on him on it.
How about demoting him? Can you do that, and then hire a new Assistant Manager or promote a different person?