Yes, insha Allah. Every time one will use that Qur’an for reading it will generate good deeds for you as one who donated the Qur’an and for him as he was intended in it.
Allah says: “And we document that which they have presented and that which was of their marks” (Yaseen 36:12) which means the marks of good deeds left after people from you especially family will be considered yours.
Also the Prophet (peace be upon him) said: “If a person dies, his deeds will cease to generate rewards except 3: knowledge, a continued Sadaqa and a righteous son making Dua.” This deed includes the three together: a family member, knowledge of Qur’an and Sadaq Jariyah.
Almighty Allah knows best.