Find the wish you want to mark as 'Bought by myself'. Press the icon with the three black dots on the wish and select 'Delete wish' marked in red. You now have the option to choose 'Bought by myself'. Confirm your choice, and the wish will now be listed under 'My gifts' in the menu in the top right corner.
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Find the wish you want to mark as 'Received as a gift'. Press the icon with the three black dots on the wish and select 'Received as a gift'. The wish will now be listed under 'My gifts' in the menu in the top right corner.