Charles Ellicott Commentary Exodus 4:15

"And thou shalt speak unto him, and put the words in his mouth: and I will be with thy mouth, and with his mouth, and will teach you what ye shall do." — Exodus 4:15 (ASV)

Thou shalt ... put words in his mouth, that is, tell him what he is to say—provide the substance of his speeches, which he will then clothe with appropriate language.

With thy mouth. —Suggesting the substance to you.

With his mouth. —Suggesting the language to him.