You pay tax on all income earned in your country of residence. I'm guessing your friend still intends on living in Ireland, therefore they will have to declare this income. Since it's only 16 hours, I imagine the entire welfare payment wouldn't be lost.
Provided the 16 hours aren't spread over the 5 working days, he may still have an entitlement to some Jobseeker's payment. He cannot claim for any day that he has work - even if it's only an hour or two. The best set up is 16 hrs over 2 or 3 days, and claim for the remainder of the days.