In Texas,

I've had a tenant for almost 2 years and she leased the home because she and husband were separating. I found out later that they decided to reconcile, however she never added him to lease.
Recently (past 3 months) the rent has been late and in tracking her down ended up finding out he was paying rent because she decided to leave and live with her sister although her furniture is still in house.

He wants to sign a new lease with me in his name and stay there. She has 1 month left on lease but technically she hasn't been paying. Can I terminate her lease agreement and sign new lease with him?

Also, need to know if I can keep her security deposit since she broke the occupants on premises, late payment, 2 dogs without permission, and some damage to backyard fence.

Send her a certified letter stating that you are not renewing her lease and that she has 30 days to return the keys. After the 30 days have passed, you can sign a new rental agreement with the husband.

You can only keep the deposit for damages, late rent, etc. If it only costs you $100 to fix the fence, then you would need to return the rest of the deposit. Not sure on your state laws, but most of them have a 21-day rule; you need to either return the deposit in full or send a letter stating why you are not returning it within 21 days of the tenant leaving the property.

Since its only one month, I would do as This8384 advises and inform her you will not be renewing the lease. Then you can prepare a new lease for the husband and have him sign to go in effect after the expiration.

But I'm wondering why you would want him as a tenant if he's been paying late.

As also noted Security can only be used to pay for damages and unpaid rent. You need to send the tenant a letter within the legal timeframe explaining what the deposit was used for and a refund of the balance (if any).

But I'm wondering why you would want him as a tenant if he's been paying late.

You never know; he could have been giving his ex the money for the rent and it never made it to the OP. Or maybe the ex told him she was paying it when she wasn't.

That or this poor OP is going to get screwed again.

You never know; he could have been giving his ex the money for the rent and it never made it to the OP. Or maybe the ex told him she was paying it when she wasn't.

That or this poor OP is going to get screwed again.

I thought of those possibilities, they certainly may be the situation.