can i give an app to a family member that I already purchased for myself?\

If you have purchase sharing enabled then family members should be able to access your unhidden past purchases. There are a few apps which are ineligible for family sharing, you would need to check the details of the specific app in the App Store.

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You cannot transfer ownership of a purchase. It may be possible to gift the app but I haven't done that with Family Sharing so I can't say offhand how it works if she already has a copy she can download from another family member's shared purchases. To find out for sure, clearly outline the situation to a person at Apple Choose your country or region - Official Apple Support

Gift apps, music, movies, and more from Apple - Apple Support