The prophet PBUH used to frequently visit the graves. He additionally used to made Duaa for them on said graves saying:
“Al-salaamu ‘alaykum ahl al-diyaar min al-mu’mineen wa’l-Muslimeen, wa inna in sha Allaah bikum laahiqoon, nas’al Allaaha lana wa lakum al-‘aafiyah
(Peace be upon you, O people of the dwellings, believers and Muslims. If Allaah wills we will join you. We ask Allaah to grant us and you safety)
Reading Quran on the graves was never reported by the Prophet nor his Companions. This doesn't mean it is forbidden, at most it would be a biddah (innovations). If doing this will make your friend feel better as a way of a coping mechanism, I don't see the harm in doing so. There are many Biddah in Islam, IMO if it does not interfere with the creed and does not hurt anyone, go for it.
If anything, at minimum your friend will get rewards for reading Quran for 40 days, I do not know but I doubt your friend reads that much Quran (I know I don't) normally.