If it has any bearing on how Moses originally prayed, currently Judaism has 3 daily prayers:
Sacharid, the morning prayer
Mincha, the afternoon prayer
Maariv, (Sounds like the Muslim 'Maghrib'), the evening prayer
When we compare these to the 5 salahs of the daily Muslim worship, the most striking difference is that the Jews lay flat on the ground with forehead to the ground in their Sujud (prostration) in the Jewish worship as demonstrated here and here.
The Jews bend down for what appears similar to the Muslim Ruku, demonstrated also here, but they conclude their prayer by performing selawat to both sides while they are in ruku position whereas Muslims conclude with selawat kneeled in the sitting position.
I believe the Sujud is the most important part or climax of the Muslim Salat. I could not find references to the Sujud in the Old Testament but in the New Testament, Jesus (Isa ibn Maryam) is mentioned putting his forehead on the ground in the gospels. The complete Muslim salah was presented to Muhammed pbuh when he went up on Miraj (the night ascension). Originally the qibla was toward Jerusalem, but some time later switched to Mecca.