Is it linguistically permissible to write "رَبِّي" (my Lord) instead of "رَبّ" (Lord), and why was it written in the Qur’an as "رَبّ" and not "رَبِّي"?

It is not permissible to alter the spelling of the letter 'ya' in the Mus'haf, because the orthography of the Qur’an is divinely ordained. The proof for this is that it was written with this spelling during the time of the Messenger of Allah, peace and blessings be upon him, and he approved it. The practice of the Rightly Guided Caliphs continued upon it, and there is a consensus on it.

As for writing it as it is, this is a permissible and well-known matter in the Arabic language, and it exists in the Noble Qur'an. The omission of the 'ya' of possession is more frequent in it.