Inherited Tenant Problem Questions:

[Jonathan Johnson]

Hello BP,

I've inherited some unsavory tenants. I was mostly fine with it because all the leases were going to be up in July or sooner. HOWEVER, I was not aware about just how bad it was.

Tenant 1 - wanted to talk to me in private. He's a college kid, prepaid his rent for the next two months with the last landlord, his apartment was a mess, and... he's registered with a possession of child pornography crime. He was very honest and upfront with me and I think his parents help him pay his rent.
I have a baby girl and we are moving right across from him. We are not ok with him staying. In his lease, the last landlord included this paragraph:

My question: According to this, do I just give him a letter stating we are terminating his lease? What do I do with the prepaid rent? His deposit is fine because there doesn't seem to be any repairs needed. 

Tenants 2 - Boyfriend and Girlfriend. Boyfriend was recently incarcerated, and will be for a long time. Tenant 1 says the girlfriend already has a new boyfriend and hasn't been seen in a week or two, which isn't too long but is concerning. Their lease is up in July, but I'm having a hard time figuring out how that's going to play out with all his stuff in there. Should I just get them out now?
What if she just dips out? They are both on the lease. 
Do I need to do something specific with his stuff if she dips out and leaves it all there?