Tax Resident in Ireland,Working in Northern Ireland

Hi, hope someone can help. I am tax resident in southern Ireland. I spent part of this year working in South, then a period of 5mth working in North. I am now due to start work again in South. During my 5mth period I paid UK Paye & availed of UK Tax credits. I understand I will be eligible for cross border relief so will have no further Irish Tax liability on this income. However now I am returning to work in the south & have 5mths of Irish tax credits which I have not utilised...can I use these or are they void as I had UK tax credits for that same period? Should I use my P45 from 5mths ago when starting new job, which will effectively result in a tax refund??

AFAIK, you declare all income for the year on your Irish tax return, and your tax bill is calculated.
Then the tax you paid in the UK will be deducted from this bill.
Therefore, the total tax you will pay, will be as though you earned all your
income in Ireland.

The tax agreement between the two authorities is desigend to ensure that you cant use both tax credits to reduce your tax bill.