It really should be a gun trust to do this. The internal verbiage is different in some areas and it has multiple schedules. A trust is considered a US person (entity) and so can purchase the NFA item. The trust has flexibility built into it that and individually purchased NFA item doesn't. It allows for multiple people to access and use the NFA item, adjustment of who those people are, and flexibility to adjust who gets what at death of the trustee. This last point is huge and simply cannot be overlooked. Probate court for your relatives is a crappy way to go out. If you buy an NFA item and then want to put it into the trust, you have to transfer it and pay another $200 and wait for the Form 4 to clear before it will be in the trust.
As it stands now, Trusts and LLCs are the only avenue around Sheriff sign-off on the Form 4s for purchase. Oblowme's recent bout of executive order douchbaggery will effect trust purchases, but I haven't been able to get the actual wording of what will change in the future and can only work off of rumor. So, instead of passing bad info, I won't discuss what I've heard. Some of it doesn't sound good though.