All perfect praise be to Allah The Lord of the Worlds and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Based on the above question, it is evident that the Islamic bank is going to buy the house from its owner and pay the value of the mortgage to the non-Islamic bank. This form of sale is permissible because, in principle, transactions are lawful and this form doesn`t entail any violation of Sharia.
In conclusion, there is no harm in carrying on with the transaction mentioned in the above question. And Allah knows best.