Can I make amendment to the lease that I inherited from previous landlord?

[Sara T.]

I just got a rental property that comes with a tenant who is now on month-to-month lease. The previous landlord only collected half month rent as deposit, and I would like to increase the deposit to standard one-month. I'm thinking if I ask the tenant to pay the other half, I'll probably need to make an amendment to the lease to reflect that. But since the lease was signed between the previous landlord and the tenant, can I still make the amendment to the same lease? How would you go about that?