Should I let my tenant sublet?

[Emily B.]

I have tenant who signed a lease in August. He got a good deal-- $150 under what the same apartment rents for in the rest of the property (it's a quad). I did this to avoid vacancy. But he never moved in. A few things are there-- a partially unboxed sofa, some cleaning supplies, a towel-- but there is no evidence of him every staying there overnight. 

This morning he texted me saying he has a new opportunity in Boston and asking if I'd be open to him subleasing it. I don't like the idea of putting the choice of tenant in his hands (without a background check and my vetting). I also don't like the idea of trying to find a tenant myself in December/January. 

What should I do? Should I find a tenant myself on the condition that he continues to pay the rent until the person is placed? (In which case, could this be a good opportunity to raise the rent?) 

Should I say sorry, your sh*t out of luck, you need to carry the lease to term? 

Are there other options I'm not considering?

Thanks so much for your help. 

- Emily 
P.S. There's a clause in the lease that imparts a $1000 penalty for breaking the lease but clearly he's not aware of it. 

[JD Martin]

No. Either he pays the early termination and you guys go your separate ways, or he pays the rent while you look for a new tenant and then he goes on.