Should I allow tenants to sublet or find a new tenant?

[Lisa Montana]

Some great tenants just told me that the offer they made on a house has been accepted. They've given me more than 60 days notice and offered to find subletters or new tenants to move in on April 1, so there would be no vacancy. Their lease allows subleasing with the landlord's prior written consent. Is it better to let them sublet or allow them to break their lease after they find a new tenant? Either way, I would run a credit and background check on the subletter or new tenant. One of my concerns is that I'm in the process of refinancing the property and sent the lender their 12-month lease. Hopefully, the loan will close long before April 1, so this might not be an issue. Thanks in advance for any input.