Yeah, the price of being on EASA-reg
An 8130-3 form is not usable with a
secondhand part, even if the secondhand part has been yours and yours alone since it was new
So you have to "process" the US-serviced part through an EASA-145 company, which "inspects" it
tests it
and then spends £0.0000001's worth of laser printer toner to print off a fresh EASA-1 form. Their hefty charge goes towards their mandatory contribution to the UK CAA pension fund.
Of course I would never suggest doing anything off the books
Paperwork always comes before safety, and quite right too.