Salat can be offered on behalf of a deceased in Islam, e.g.,

السيد علي بن طاووس في فلاح السائل: عن حذيفة بن اليمان قال:

قال رسول الله (صلى الله عليه وآله): ” لا يأتي على الميت ساعة اشد من اول ليلة، فارحموا موتاكم بالصدقة، فان لم تجدوا فليصل احدكم ركعتين، يقرأ في الاولى بفاتحة الكتاب مرة وقل هو الله احد مرتين، وفي الثانية فاتحة الكتاب مرة والهاكم التكاثر عشر مرات،

Al-Seyyid Ali Bin Tawoos, in (the book) ‘Falah Al-Sa’il’, from Huzeyfa Bin Al Yaman who said,

‘Rasool-Allah^saww said: ‘There will not come upon the deceased any time severer than the first night, therefore make your dead ones happy by (giving) the charity. So, if you cannot find (it – the charity), then let one of you pray two Cycles Salat reciting in the first, the Opening of the Book (Surah Al-Fatiha) once and Say: ‘He, Allah, is One [112:1] (Surah Al-Tawheed) twice; and in the second (Cycle), the Opening of the Book (Surah Al-Fatiha) once, (and) The augmentation diverts you [102:1] (Surah Al-Takasur), ten times.

ويسلم ويقول: اللهم صل على محمد وآل محمد، وابعث ثوابها إلى قبر ذلك الميت فلان بن فلان،

And he should perform Salam (at the end of Salat) and say, ‘O Allah^azwj! Send Salawat upon Muhammad^saww and the Progeny^asws of Muhammad^saww, and Send its Rewards to the grave of that deceased, so and so son of so and so’.

فيبعث الله من ساعته الف ملك إلى قبره مع كل ملك ثوب وحلة، ويوسع قبره من الضيق إلى يوم ينفخ في الصور، ويعطى المصلي بعدد ما طلعت عليه الشمس حسنات، وترفع له اربعون درجة

So, Allah^azwj will Send from that very moment, a thousand Angels to his grave, there being clothes and ornaments with each Angel, and his grave would be expanded from the narrowness up to the Day it shall be blown into the Trumpet (Qiyamah), and the praying one will be Given Rewards of the number of whatever the sun emerges upon, and forty levels would be raised for him’’.[1]

عن الصادق عليه السلام قال: لا يمنع الرجل منكم أن يبرّ والديه حييَّن وميّتَين يُصلّي عنهما ويتصدّق عنهما ويحجّ عنهما ويصوم عنهما، فيكون الّذي صنع لهما وله مثل ذلك فيزيده الله بِبرّه وصِلته خيراً كثيراً

Imam Sadiq^asws said: “You should not let anything prevent you from treating your parents kindly whether they are dead or alive. For them you can pray, give charity, go on the holy pilgrimage, or fast so that they get the reward. You will also be rewarded, and God will grant you an abundant increase in good through His Kindness and His Rewards.”

ما رواه الكليني بإسناده إلى محمد بن مروان قال: قال أبو عبد الله (عليه السلام): ما يمنع الرجل منكم أن يبر والديه، حيين و ميتين: يصلي عنهما و يتصدق عنهما و يحج عنهما و يصوم عنهما، فيكون الذي صنع لهما، و له مثل ذلك فيزيده الله ببره. و صلته خيرا كثيرا.

What al-Kulaynī narrated by his isnad to Muḥammad b. Marwān. He said: Abū ʿAbdillāh عليه السلام said:

What prevents the man from you to do good for his parents, alive and dead: praying for them, giving charity for them, doing Hajj for them, and fasting for them. That which one did would be for them, and he would have the like of that, and God would increase him with much good by his beneficence and his (maintaining of the kinship) bond.[2]

[1] Mustadrekul Wasail V-8 P-167

[2] Mustadrekul Wasail V-8 P-167, H. 14