@William K., it sounds like the PM company lied to you about payments but they were never actually made.
Step 1) get this resolved. Step 2) fire PM, if indeed they lied. But you have to resolve Step 1 first.
Do your best to be professional and reasonable so you can get this resolved as quickly as possible. Threatening the PM of termination or lawsuit will definitely not get your rent faster.
Moving forward, I would require...
Detailed Repayment Plan: Have the PM provide their course of action to get the tenant paid and whole again. If this is the PM's responsibility then they must detail the exact milestones with dates and amounts.
Penalty Recourse: There needs to be recourse for the tenant and PM to get you paid in full. Late fees need to be sent to the tenants. Start the late rent notice and eviction notice. Just because you send the eviction notice doesn't mean you have to execute on it. However, at least starting the paperwork accomplishes a few things: let's the tenant know you're serious, saves you days in case you must evict, provides comfort there's progress being made. As for the PM, I assume they aren't charging fees if rent isn't collected. But make darn sure that's the case! Their plan needs to indicate a form of fee deduction or retention until all rent has been paid. They need a penalty as well, IMO.
Consistent Updates: Now it's personal! Communicate your expectation for a consistent update, however often you want them: daily, weekly, bi-weekly, etc. I think weekly is best. Have this detailed in their correction plan so you can hold them accountable. And make them aware of a consequence if there are not consistent updates. Require them to provide documentation with their updates. If they said rent was paid, show me the proof!
Partial Payments: There's mixed reviews on BP whether you should allow partial payments or not. I'm of the opinion that some money will be better than no money at this point. In the past, I've changed unpaid rent to a longer extension but required semi-monthly payments in exchange. These tenants had been there for a year and all of a sudden were constantly late for 3-4 months. Turns out, she had a baby and her hours were cut back significantly. Therefore, we made a plan to reduce rent for 2 months until she went back to work but months 3-6 had an increase.
Embreach Notification: Review your Management Agreement for the proper procedure but immediately send them a notice they are embreach of their contract, if indeed they are. Be professional and communicate this ahead of time. I'd say something along the lines of "It sounds like you're working on a correction plan and I'm confident your team can get this resolved. However, I am advised to submit this embreach notice now so we can follow the proper protocol of contract." Similar to the late/eviction notices, just because you sent notice doesn't mean you have to execute any further actions. But delaying the notice only protects the PM company, not you.