Just talked to Suzy at HPD firearms
she said no need go back to HPD with the signed PTA. the seller will send it in to HPD.
but take a pic of the signed PTA so you have the permit #, that you will need for the filling out of the online form
fill out everything on the online form, if you don't it will be invalid
you do everything correctly and fill everything out , just register online. no need go back to HPD