Customs procedure Learner

Shortly to start moving goods GB to NI. Once we have registered and been approved for UKIMS, when we send our goods to Northern Ireland NI and declare them at risk, pay the appropriate duty, etc.,
I understand that we can move them freely around Ireland.
The query is that when we invoice a trader in Southern Ireland SI for these declared and duty paid goods is the VAT rate 0%. (We have registered for the XI version of our GB Vat code.) In simple terms how is VAT accounted for movements between NI and SI does the NI seller add VAT to the sales invoice when selling to the SI customer?