Tenant on Vouchers, Accepted Partial Payment - TENANT PAST DUE

[Reece Bierhalter]

I have a tenant that is under a housing voucher (HAP Voucher).  I get a direct deposit from the city they are in the program under every month, and the portion of the rent the tenant is responsible for is then paid directly to me by tenant.  Every so often, the voucher contract is reevaluated based on changing circumstances and the tenant/Housing Authority split will change.  Long story short, the amount had changed a couple of times, and I picked up the tenant portion of rent (via a MoneyGram money transfer) and went back to the contract to verify if it was the right amount.  It was short by $200. Had I realized it wasn't the full amount, I probably wouldn't have picked it up in the first place, but that ship has sailed.  Initial late fee is $150.  Tenant paid me $200 on the 4th, and asked if the late fees would stop.  I informed tenant that according to the lease, all payments are applied first to non rent related charges then to rent and late fees would only stop once tenant was current on account.  So that $200 payment was applied first to the $150 late fee, then the remaining $50 to rent.  So now on the 4th tenant is $150 short on rent, and every day an additional $20 late fee is added until account is current.  It is now the 16th and I still have not heard from tenant, and I have provided tenant with updated late rent notice every day with updated amount to which tenant has not responded to.  Knowing that I have accepted partial rent payment, Can I or Can't I post and enforce a  "# Day Notice To Pay Rent or Vacate" ?  This is in TEXAS.  I am quickly learning that there is a better way to handle this altogether from the beginning, but I am needing to fix this now, and can't change what I have done.  Thanks for the help in advance.  Side note, this tenant has also just lost their Housing Voucher, so I have a feeling I may have to evict said tenant sooner or later because they no longer have the rent supplement.