Is it permissible to gift a Mus'haf (copy of the Quran) or a part of it to someone with the intention of making the reward of its recitation an ongoing charity (Sadaqah Jariyah) for a living person, and is it permissible to buy prayer beads (tasbih) and make their reward for a living person, and what are the best deeds that can be done and dedicated to living people with the intention of goodness, guidance, and forgiveness for them?

It is permissible to dedicate a Mushaf (definition) (copy of the Quran) as a waqf (endowment) and assign its reward to the living or the dead; this is considered an ongoing charity (Sadaqah (definition) Jariyah), as is the endowment of parts of the Quran. Similarly, it is permissible to dedicate a prayer beads (subhah) as a waqf and gift its reward to others, whether living or dead, because its use in acts of obedience is legislated. The best deed whose reward can be gifted to the living is sincere supplication (Du'a) and seeking forgiveness for them.