From the UK Border Force Manual:
muzzle loading long arms are considered Section 1 firearms.
3.2 Documents required for an accompanied import of a firearm from a
non-EU country by UK residents.
3.2.1 Private individuals
Private individuals require one of the following documents:
• UK Firearm Certificate, or
• Shot Gun Certificate.
In the case of a newly acquired firearm the importer must have entered details
on the Certificate and, in the case of a firearm, the Certificate must be preauthenticated by the Police giving prior authority to acquire or purchase the
type of firearm being imported. The Police Firearms Licensing Manager for
the importer’s UK address must be notified of all importations.
It is the customers problem, but not easily addressed. You get payment, ship the weapon submitting customs paperwork for the USPS or whoever you use to ship, and in order for the customer to receive the package he has to have all the paperwork in order.