Peace.
A major problem with your hypothesis is that the Muslim method of prayer has been practiced since the early days of Islam in Mecca, not after migrating to Medina/Yathrib 13 years later.
As for similarities, when God is the source of the teachings of all the prophets, there are bound to be similarities in worship. The Qur’an itself claims that it contains within it those teachings from the former Scriptures which were of a lasting value:
[98:2-3] A Messenger from Allah, reciting unto them the pure Scriptures. Therein are lasting commandments.
Infact, if Islam taught that the way to approach God was opposite the way the former prophets approached God, then it would be open to question. If God is the same, and human nature remains the same, then the way to form a relationship with God should not be fundamentally different, nor should the scriptural teachings be vastly different.
However, some people do not realise this point, and erroneously charge Islam with having copied the scriptures and practices of the former peoples. This charge is actually a proof of it’s truth, not of it’s falsehood. For instance, about the practice of fasting, the Qur’an categorically states that:
- [2:184] Fasting is prescribed for you as it was prescribed for those before you*, so that you may become righteous.
Why would Islam teach similar ways of forming a relationship with God, if the purpose of Islam was not that very same thing?
Peace.