OK - that is quite complex.
He is doing two things - he is purchasing a one half share in an investment property and he is buying a new PPR. ( I am assuming that when you say a new house, you are referring to a new build?)
There is no stamp duty on the purchase of a property worth less than 125K so it is possible that he will pay no stamp duty on the buyout of the apartment. He will need to get a valuation for Revenue if he is claiming the value to be below 125K. Revenue are desperate for money at the moment and I find that anything I am submitting is being queried.
So long as the new house is a new build and below 125sq. m , and he is a bona fides owner occupier, he will not have any stamp duty. If its not a new build or he is an investor, he may have stamp duty liabilities.
A good starting point is Revenue Stamp Duty Guidelines - SD10A- downloadable from Revenue website.
mf