The prevailing wisdom is that EASA accepts an 8130-3 for all new (i.e. unused) items.
Some UK maintenance people add that the 8130-3 must be from the original manufacturer.
I don't have a reference for the above, although the first one is probably true and the other one is probably "revenue generation".
A while ago I compiled these notes but a lot of them will now be out of date, due to EASA.
However, they do deal with the myth that only specific forms are acceptable and the only components which may be installed have to come with those forms. That was never the case under FAA and was mostly not the case under JAA, though great many people in both camps still believe it - not least because everybody makes more money that way.
Recently, speaking to an EASA firm, Subpart F I believe, this procedure (10MB PDF) has come to light which, on the face of it, enables an EASA Part F company to convert an 8130-3 into an EASA-1 form. This would enable an 8130-3 which accompanies a used (e.g. overhauled) item to be installed on an EASA-reg plane.
It appears to be a most useful concession, especially where the overhauled item has been yours all along and you had it overhauled by a reputable shop in the USA, and it is "used" only because it was overhauled. Not being able to overhaul your own stuff by reputable US shops has been a long standing farce with Part M. The best shops in the USA are not EASA approved and cannot generate a dual release 8130-3.
Any views?
Not all 8130-3 are acceptable.
A EASA company could recertify a project. But I guess it is not strange that this isn’t done (often / or at all?)
Take this example, you have a not acceptable 8130-3 because the repair station overhauld you gyro, and the company was not accepted by EASA. You would have the gyro overhauld their because it was cheaper / better / what ever.
Then a EASA company needs a C rating, pay a lot to EASA to have that rating, educated their staff, have all approved data to overhaul this P/N. So they also could overhaul this item.
They could issue a Form 1 for the item overhauled with the non acceptable 8130-3. But that would ruin their own business, and they would take responsibility for it, for a bit of money. It doesn’t make sense too do so.
It depends on how much money the firm has 
I have seen a propeller “passed through” an EASA145 company, to convert an 8130-3 to a JAR-1 form, for about €4000.
Smaller parts can be processed for a few hundred €.
What do you think of that PDF I posted above? It means one can convert an 8130-3 into an EASA-1 without needing an EASA145 company. That is potentially massively valuable to an aircraft owner on the EASA reg.
What do you think of that PDF I posted above?
The form still can only be issued by an EASA approved company. That it hasn’t got to be Part 145 doesn’t matter much in my opinion. The limitiation for used parts will then also be that they are for non commercial aircraft as well, though this is not a problem for most GA offcourse. Note that the company that issues the form still have to be rated to do so. This rating means that they would also be able to perform the work themselfs.
In my experiance, it would be less expensive to have it serviced there at once. Altough prices in the US are often lower, people seem to forget about shipping, connectors, adapters, racks, import taxes, and recertification. Customers who “arrange” their own avionics will pay more than they expected because they forgot about a lot of things. Often it is also more expensive than when bought directly at the installer / shop.
I am not 100% for the 8130, for EASA form one, only a manufacturer can issue a form stating that the part is new, others could only state, repaired, inspected / tested or overhauld. I could imagine that this is the same in the US.
It turns out that the route in post #1 very much exists.
It is based on a permission issued by the national CAA. Different Subpart F companies got different levels of authority to do this and the early ones got much better right than later ones. It started when EASA started i.e. about 2003.
The more general case of a non EASA 145 company issuing an EASA 1 form is a different thing – that is often done by renting a 145 company’s laser printer renting a 145 company’s approval and this is “okay” because, ahem, hmmmmm, there is an audit trail so “it must be good” 
