Hi, thank you for your question. This would be transfer of share from him to you and can be done using the process outlined here: https://www.gov.uk/registering-land-or-property-with-land-registry/transfer-ownership-of-your-property
You will also need to consider whether you wish to hold the property as joint tenants or tenants in common with your mother. Joint tenants cannot pass on their share to other people as inheritance and it automatically transfers to the other joint tenant upon death, whereas tenants in common can pass on their share in a will or under intestacy rules.
Given the potential legal complexities it would be best if you instruct a local conveyancing solicitor to deal with this to ensure that it is done correctly.
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