This is not legal advice but I will give my professional opinion, as a property manager. First and foremost, accepting even a partial payment after the cure period has lapsed is not a good idea unless you are in a state that specifically allows such.
@Peter M. - Peter is accurate, not all evictions are related to payment... but you need to give the tenant clear notice OF WHAT they need to cure during their right to cure period. If you solely told them "you need to pay rent" then that is likely, YOUR sole argument to the court. Now if they also, for example, punched an employee you should include the termination for clear and present danger language. Not seeing a way to cure that one! I would not walk into a court-room with the "they breached their lease" argument without strong evidence of their continued/uncured breach...
When you say "filed the eviction" do you mean you served the tenant a Pay or Quit, filed the Forcible Entry and Detainer motion with the court, or have been granted the FED motion and have now filed the Writ of Removal?
Based on context, I am assuming that you have just filed the motion with the court. If that is the case, and you have accepted payment I would dismiss the eviction, immediately. To me the premise of your FED (the amount outstanding) is now incorrect (...probably).
If you decide to continue with the FED, let's assume the judge rules in your favor... that ruling is likely because the tenant did not show up for court. You filed your notices correctly and timely, reported the cure amount accurately, and avoided the fact you collected a partial payment. The tenant will likely still have the option to appeal... at the appeal hearing, the tenant tells the judge that you accepted payment in full for the rent, that's why they didn't come to court... The outcome is not likely going in your favor at this point. Regardless of the outcome, you have a very upset tenant occupying your property and an appeal window that will potentially take several weeks (or months). If they decide not to appeal, they still have possession of your property until the Sheriff gets around to scheduling the Writ of Removal... which they will likely protest on the same grounds.
I would not want to be in the courtroom when the judge/magistrate hears you accepted more/less full payment and evicted anyway. As such, I would not suggest continuing with the FED now that you have accepted payment. Instead, try to negotiate a peaceful move-out and file a new / accurate FED if any breaches still exist.
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Insofar as the late fees: Generally, we do not include our late fees in our cure notices as they can be interpreted by the the court very differently, depending on area. Our counsel has strongly advised against including late fees... FED is meant to deliver you possession, don't bog down the mission with a few extra dollars of fees. You can bring the summary of all damages later via a money judgement motion.