Dear Rabbi. On shabbos morning if someone will miss the time of gra to say shema with brachos and is relying on the time of magan avraham, should one say shema in time for gra time without brachos, before davening?
You most probably mean the opposite, because the zman of the Magen Avrohom is earlier than the Gr”a. Regardless you are bringing up a good point, and yes if one sees that he will miss the zman of the Magen Avrohom he should preferably say Kriyas Shema beforehand, even though it is without the brachos. Then later on he will repeat the shema with the brachos. It is also preferred to have in mind when saying both shema’s that you want to be yotza with whichever reading is the correct one, and that the other one is not to do the mitzvah.
Rema O:CH 46-9, R’ A. Eiger ibid.