How Saint Moses became a saint?

If you are taling about Moses from the Old Testament, personages from that time frame are not usually given the title of saint.

However, there is a New Testament saint named Moses, the Apostle of the Saracens.

Moses was a hermit in the area between Syria and Egypt. He evangelized the nomadic tribes in the Syro-Arabian desert. Mavia, their queen, agreed to this on the provision that Moses be named their bishop. Moses agreed, but a controversy ensued when he refused to deal with the archbishop of Alexandria; the archbishop had jurisdiction over the area, but was supported Arianism, which made him a heretic to Moses. Later consecrated by an orthodox bishop, Moses spent the rest of his life teaching and preaching to the nomads. He negotiated a lasting peace between the nomads and the Roman empire. He died about the year 372.

Moses was a pre-congregational saint who lived and died at a time in the early Church when no formal proceedure for canonization existed. he would have been acclaimed by the people as a saint to the local bishop who then would have approved him as a saint.