(co) Landlord Agreed To Early Move Out Prorated Rent For Last Month, But Wants Me To Pay In Full And “refund” Me The Prorated Amount Later?

LL agreed in writing to prorate last month as I’m moving mid month. Agreed to earlier move out date in writing. But wants me to pay the month in full and “refund” me the prorated amount. In our lease there is already language about the prorated /per diem rate. There is nothing in the lease about “refunding prorated rent” after move out…. In the lease it clearly lays out the simple math “per diem rate $ x days = total prorated amount due”

Do I have to pay in full for the last month or can I just do the prorated amount for the last month? For reference, at move in, the first month was prorated, and I did not pay in full and get “refunded”, I just paid the prorated amount as calculated by the lease. So being refunded rent would be a change from our lease and history of prorated rent calculations.

I do not trust this LL at all to refund my money and would prefer to give them only the prorated amount. Would I be wrong legally to only give prorated amount? Thanks in advance.