Yes, when you are reporting the sale, you can add the Improvements to your Cost Basis, reducing your gain on the sale. However, if this was your primary residence, your gain may be excluded anyway, you are just reporting.
Your partner would not add the Improvements to their Cost Basis when reporting the sale, so will have a larger gain than you. Once again, all their gain may be excluded.
Here's more info on the Home Sale Exclusion and Sale of Primary Home.
@Mannyac
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