I'll take a stab at it and keep in mind, I've only done 1...so anyone that reads something I don't have quite right, please correct me.
First off, the seller initiates the Form 4. It's easier to be together in one place to walk through and pass the computer controls back and forth. You could do it through a Teams/webex/etc type software too...but in person would be my preference. There is a lot of personal information (think all the stuff you had to give the NFA originally), that is associated with these Form 4's. I don't really want that information from the buyer to enter on the form 4 on his behalf.
The buyer needs a picture of himself, ETF file of fingerprints and trust paperwork all saved somewhere it can be accessed and uploaded/attached to the form 4.
The seller need the original stamp paperwork/email to make it easier. You search using numbers on the approval data to "look up" the suppressor and associate it to the transaction/form 4 you're filing out.
Then it's a matter of initiating the Form 4 through eforms and passing the computer controls back and forth to enter or attach the information.
Once certified, both of you will be notified via email. I hope this helps a little bit, we weren't as prepared as we should've been when I did it and this information would've been helpful to know/understand.