Tenant Breaking Lease Early Question

[Melissa B.]

My tenant signed a 1-year lease and is leaving eight months early. Here in Arizona, the law is that we have to make reasonable attempts to find another tenant to replacement the tenant (but not in any way that would harm any of my business, lower the standards of the tenants, lower the rent, etc.) Until we find a suitable tenant (and their lease starts), the tenant is responsible for the rent. I cannot legally have two leases for going on at the same time, so what can I have the current tenant sign that says their lease now ends as soon the beginning of a new lease by another party begins or when their current lease ends, whichever is sooner? What would a document like that be called? Thanks.