Ad Jesum Per Mariam - To Jesus, through Mary.
The Church teaches that Mary is our mediatrix with Jesus, and Jesus is our mediator with God the Father. So any prayer offered to Mary doesn’t stop at her, but goes to Jesus.
We can think of it as offering it to Mary who immediately takes our prayers and our intentions to Jesus. Those of us who do Marian consecration give ALL of our prayers to Mary, not just rosaries, with the intention that she will take them all to Jesus.
Alternatively we can think of it as our prayer going straight to Jesus, but we also ask Mary to specially present our prayers to him.