Capital gain tax on property sold by deceased person

My Father sold a house, co-owned with my Mother ( 50:50) , in March 2018. Each of them opened a Capital Gain Account with me as the Nominee ( two accounts opened, one in my fathers name and the other in my mothers name), intending to buy a new house . My father passed away in October 2018, my father had made a will before the house was sold, in which it was stated that his share in the house should go to my mother, but the house was sold when my father passed away. The will further goes to say that " I bequeath all the other residual property , assets and other rights whether or not existing at the time of my death to my son and daughter", does this mean that the amount in the capital gains account to be distributed between me and my sister? My question is If I and my sister invest the proceeds from the capital gain account , into buying another house jointly with my mother , will I have to pay Capital Gain tax which my father has to pay due to closure of his Capital gain account? In fact me and my sister wish to give the proceeds od the capital gain account to my Mother, so we can buy a house in her name. Guidance on whether Capital gain tax has to be paid on behalf of my father on closure of Capital gain account , even if we( legal heirs ) buy a house from the proceeds , is appreciated.