In reply to supersteve:
Which Ireland are you sending to?
(Just for background my only experience is EU to England, so no expert but this would be my understanding based on what I've picked up over the last 4 months)
Republic - My understanding is that you need to avoid it officially entering the UK, then it's an eu-eu shipment so should be exempt of any charges.
Northern - yes you will need the certificate of origin showing it was manufactured in the EU, in order to avoid paying duty under the new post-brexit trade agreement. Also tell them to check out postponed vat accounting. You will probably still have customs charges (maybe £50) to cover them doing the paperwork when the goods enter the UK.
If possible, make it sure it is direct ship from the EU. Importing to the UK, then re-exporting to the Republic could lead to import duty being charged (not my area of knowledge). Even if you are shipping England to N Ireland you need to complete a heck of a lot of paperwork (that promise of no border in the Irish sea was a lie), to prove the goods will remain in the UK and not jump across the land border into the EU, so avoid if possible.