Is it permissible to gift a painting inscribed with "O Allah, open for me the gates of mercy; O Allah, open for me the gates of provision" to a friend who has opened a shop selling doors?

There is no harm in writing and hanging supplications (du'as) and remembrances (adhkar). Jurists have stipulated that it is disliked to write the Holy Quran in places of disrespect. However, writing other forms of remembrance is not disliked unless it is in places that are trampled upon. Since what is hung is not trampled upon, there is no objection to gifting plaques containing supplications or remembrances.