Additional property higher rate stamp duty refund

[dermvc]

I would be grateful for any clarification on the following issue
My mother lived in a flat which was her primary home for many years but following my father's death, she moved to a house owned by my sister. Her flat was rented.
Following a period of ill health, she moved again to live closer to me and bought a property. As she already owned a flat, she had to pay the additional property higher rate stamp duty. The plan was to claim this back after selling her original flat but her health deteriorated expectedly and she died before the flat was put on sale.
I am the executor of her estate and the original flat has now been sold on behalf of the estate. I presume it is not possible as an executor to claim back the higher rate stamp duty on the property where she lived at the time of her death and was primary home
Thank you

[bd6759]

Timeframe is important here.

[dermvc]

Thanks
The flat was bought in 1991 and the "second" property in November 2022