Inheritance and Invesment in Property

Assalaamu alaikum Mufti

My mother currently owns her house. My sister now has spent money renovating my mother’s house and she considers it an investment and not a loan and upon my mother’s death / sale of the house she wants to be paid out for her investment in the property.

Please let me know if I have this correct.

Say the house is worth R1 000 000 (valuation done by independent party) before the renovation. My sister spent R50 000 on the renovation and the house is worth R1 100 000 (valuation done again) after the renovation therefore the house increased in value by R100 000. This is 9.09% of the new value of the house. Say when my mother passes away, the house is valued at R1 500 000, then 9.09% of this is due to my sister which is R136 363.64. The remainder of R1 363 636.37 would then be split according to Shariah amongst the heirs as this portion of the house belongs to my mother.

Is this correct?

Also how would she state this in her will / or Islamic Contract?