Law is very clearly intended to be the origin of behavior!
Not in the way Sartre was talking about. Surely you of all people here understand that.
When a guest comes to my home I might ask them to remove their shoes and they might do so. My request was not the origin of their action by Sartre’s definition, though it certainly impacted their actions. Instead it was ultimately their choice, their mind, their animus, their internal decision making that determined whether they would comply with my request.
You keep sloppily conflating the internal expression of will and external influences on behavior. If this were a colloquial conversation I would agree that law is intended to impose certain actions and inactions on people. However, you have relied heavily - almost exclusively - on Sartre’s commentary on the subject, and when he speaks of origin of action he is referring to internal motivation, not merely influence. He is making a point that actions are not preordained and that a human has choice - thereby freedom - regardless of the situation.
Law is absolutely intended to influence behavior - and indeed is blunt and heavy-handed in so doing. Law is unable and generally not intended to impact human mental autonomy and intention, except to the extent that people respond to threats.
If you want to use the common vernacular and mash together the two concepts then you cannot use Sartre’s formalized definitions and extrapolate using his jargon.