What the term means is the transfer of a particular asset (in this case the asset would be the property) by the personal representative of the estate (normally the executor) to a beneficiary under the terms of the will, in order to satisfy the legacy in the will of the deceased. It is an alternative to paying (part of) the legacy in cash. The right of the personal representative to appropriate is conferred by section 41 of the Administration of Estate Act 1925.
You will now see that a couple of questions arise.
1) Who is the executor of the estate? - you?
2) Was the property specifically left to you in the will? If not, I know of no reason why the executor could not appropriate the property to you - the value of the property appropriated would have to be agreed between the parties though the value already established for probate purposes seems right.
3) Why is the sister in the property at all (unless she was already in it and living with her mother prior to the death).
CGT doesn't come into it for you, and it only potentially applies to the estate of the deceased in the event that the asset (the property) has enhanced in value since the valuation established for probate purposes. Even then, the estate of deceased is entitled to the same 'annual allowance' of capital gain of just over £10k that an individual is entitled to.