To pass on the reward of physical and financial ibaadat (worship) to other Muslims is permissible, and the thawaab (reward) reaches the person whom it is passed to. This is proven from the Qur'an, Hadith and rulings of the Jurists (Fuqahaa). The Noble Qur'an has ordered Muslims to make du'a (supplicate) for each other. Namaaz-e-Janaazah (funeral prayer) is made by Muslims for another Muslim.
Hadrat Abu Hurairah, Radi Allahu ta'ala anhu, recited: allahumma in kana muhsinan fa zid fi ihsanihi wa in kana musi'an fa tajawaz `an sayyi'atihi -- "O Allah, if he did good, then increase his goodness, and if he did evil, then forgive his evil deeds." Imam Malik, Radi Allahu ta'ala anhu narrated it." ---Mishkaat, Baabul-Fitan. Baabu/-Malaahim, Section 2
Three important points emerge from this;
I. Completing physical ibaadat (namaaz with the intention of passing the reward, i.e. Esaal-e-Thawaab) for someone else is permissible.
2. Passing on the reward (Esaal-e-Thawaab) by mouth (i.e. saying, "O AlIah Subhanahu wa ta'ala! Give its reward to this certain individual.') is an excellent practice.
3. With the intention of blessings, to perform namaaz in Masjids associated to the pious elders is a means of reward.
There are many interpretations like these for this verse. FatIha, Teeja (Fatiha made on the 3rd day after a person's death), Daswaa (the l0th day after Chaliswaa (on the 40 day after), etc. are all branches of Esaal-e-Thawaab. Only the following transpires and makes up Fatiha: Recitation of the Holy Quran, which is a physical act of worship (ibaadat), and Charity, which is financial ibaadat. These are collected and their thawaab is passed on.
Source: Ja al-Haq [The Obliteration of Falsehood] by Mufti Ahmad Yaar Khan Na'imi al-Ashrafi, May Allah be pleased with him.
To be continued ...