Inherited tenant mailed more rent than is due

[David P.]

I just closed on a duplex 2 weeks ago and the long term tenant (10 years) just mailed me his rent check. The prior seller renewed his lease just last month to 1900/month which is about 1k below market. He is elderly and a bit old school and still does mailed checks. He just mailed me a check for $2,000 for the month of July. I want to just deposit it and hope he thinks he is on the hook for 2000/month. Am i in the wrong for depositing the checks as it is?   The tenant for sure was on an expired lease and month to month at that point but for the transaction to close they needed to generate a new lease for him so perhaps there was some miscommunication.