I would be skeptical of the tenant’s claim too if there were pictures, especially pictures that are dated right before the tenant move in.
Why did you replace the previous property manager?
How did the previous property manager respond to the tenant’s claim that he “was told to wait and until he is transitioned to the new property manager and then work directly with the new property manager.” If the previous PM denies this and puts it in writing, you have a strong case that the tenants are taking advantage of the situation.
How long has the tenant been there? I could believe the tenant’s story if they just moved in recently, say about a month ago and the old PM knew that the new PM was coming in in a month, but I would be more skeptical if they have been there a few months. You say the tenant is a family with children. What else about the tenant’s profile might suggest whether they are being truthful or not?
If you want to keep them as tenants because it may take awhile to find a suitable replacement, you could bite the bullet and then have them sign a current unit condition property form.
If you think that the tenants are taking advantage of the situation, you do not trust them going forward and you would not be sorry to see them go, charge them for the fix or replacement (less depreciated value) and see what happens.
BTW, how does the new PM suggest you handle this situation? what are their recommendations? just curious as a good PM is suppose to help make out of state investing passive but I have hear this is often not the case.