I was wondering how private transfers from MA to another state works.
I know that the receiving end must be an FFL, but do I have to also go through an FFL here to send it?
Fed Law applies. NO FA-10, NO outgoing FFL required, only a Receiving FFL required. Some Receiving FFLs demand that you send it from an FFL, but the laws (MGL or Fed Law) do NOT require this.
There is NO mechanism for "un-registering" a gun with CHSB when a gun leaves the state. I would suggest that you get a Bill of Sale and keep it for your records. That's it.