I submitted a PTA for a second rifle a couple of weeks after picking up my first rifle, the PTA approval email said that approval had been granted but would not be formally sent until a date 28 days in the future due to mandatory wait times.
I sent a scan of my completed PTA document from the first rifle to WLB by email and advised that this should be under my license so making me wait for an additional 28 days was not lawful. Not sure if I used the best wording but the dealer received the approved version of the PTA a couple of days later.
The completed paperwork from dealers is sent back to WLB for them to update the registry but it is the lowest priority work that they do so it can take months to never for some of this information to be updated.