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...i'm wondering how to go about it the cheapest way possible? Can i write ATF have them remove it
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You can, but that is not necessary (and they won't actually remove it from the NFRTR). Just wait...
...remove the barrel from the receiver and ship them as seperate packages to the buyer and if they violate the NFA by reinstalling it before getting a stamp its on them?
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Yes, that is an option. I would insist they go to separate addresses (since the receiver has to go to a FFL anyway).
You do not need to notify ATF to do this. You can just do it.
Or would my only option be P&W a flash can onto the installed barrel and ship it after its removed from the registry?
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That's another option.
Both of the above options are Title I (GCA) transfers.
Quoted:
Keep it or find an in-state buyer.
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Also good options.
In-state transfer as SBR would be one Form 4 directly to the buyer ($200).
Out-of-state transfer as SBR means two Form 4s (and 2x $200=$400).
The SBR wouldn't have to be transferred through a SOT (since it'll be a tax-paid transfer regardless) therefore any FFL in the buyer's state can process the transfer.
I'd list it for sale with options. Ideally you'll find an in-state buyer, but if not then you can open up your market (to other states) and/or lower the price.
Most people won't pay $400 to receive transfer of a SBR with someone else's engraving on it.
Some might pay $200 but the market is limited. (They'll have to be saving a lot versus buying a new one.)
If you end up selling it as a Title I firearm, and there's no chance you'll ever own it again, you
may want to send ATF's NFA Branch a letter advising it's been permanently returned to Title I configuration.
The only benefit of such notification is that, if another owner tries to Form 1 it again, they won't run into any complications caused by your existing registration.
Notification is not a requirement, and if you choose to send it I'd definitely wait until after the sale and Title I transfer are completed.