Is it permissible for a group of friends in different countries to complete a weekly recitation of the Qur’an (khatm al-Qur’an), whereby each of them chooses a number of juz’ (parts) and they dedicate the completion to a person of their choosing?

It is permissible for a Muslim to dedicate the reward of good deeds to a living or deceased Muslim. This is a commendable act, and the one who dedicates receives the reward for dedicating. Both the dedicant and the one for whom it is dedicated are rewarded. However, gathering to recite the Quran and dedicating its reward was not among the practices of the righteous predecessors, and it is an innovation.