Does it say in the tashahhud “al-salaam ‘ala al-nabiy” or “al-salaamu ‘alayka ayyuha’l-nabiy”?

What is prescribed is to say that which the Prophet (peace and blessings of Allaah be upon him) taught to the Sahaabah. He taught them to say: “al-salaamu ‘alayka ayyuha’l-nabiyyu wa rahmat-Allaahi wa barakaatuhu (peace be upon you, O Prophet, and the mercy of Allaah and His blessings)”. So we say what the Prophet (peace and blessings of Allaah be upon him) taught us and taught the Sahaabah, and he did not tell them “When I die, change it.” He taught it to them when they were travelling and going to far distant lands, and they would say “al-salaamu ‘alayka ayyuha’l-nabiyyu wa rahmat-Allaahi wa barakaatuhu”, i.e., they were praying for him. Saying salaam to him is praying for him, for well being, mercy and blessing. “ayyuha’l-nabiy (O Prophet)” is just referring to him; “ayyuha’l-nabiy (O Prophet)” does not mean calling him, rather they are praying for him. “Al-salaamu ‘alayka (peace be upon you)” means may you be safe, may you granted peace, well being, mercy and blessing from your Lord. It is a du’aa’ or supplication for him (peace and blessings of Allaah be upon him), not calling upon him; rather you are asking Allaah to grant him well being, mercy and blessing. If someone says “al-salaamu ‘ala al-nabiy wa rahmat-Allaahi wa barakaatuhu (peace be upon the Prophet and the mercy of Allaah and His blessings)” there is nothing wrong with it, but it is better to say what the Prophet (peace and blessings of Allaah be upon him) taught the Sahaabah: “al-salaamu ‘alayka ayyuha’l-nabiyyu wa rahmat-Allaahi wa barakaatuhu (peace be upon you, O Prophet, and the mercy of Allaah and His blessings)”. This is what the Prophet (peace and blessings of Allaah be upon him) taught to his ummah, and he died when that was the case, (peace and blessings of Allaah be upon him). End quote. 

Majmoo’ Fataawa Ibn Baaz (28/58). 

See also the answer to question no. 34535.

and Allaah knows best.