From what I can tell, Set Business Process Variables can only be used in the workflow that was directly invoked by Forms.

When Forms invokes a workflow, it passes in the FormsBPInstanceID and FormsSubmissionID input parameters, and when the "Started by Laserfiche Forms" option is selected, I believe it uses those inputs to connect the dots (i.e., get all the extra input tokens, set business process variables, etc.).

I tried the "Started by Laserfiche Forms" setting on an invoked child workflow since those still show "FormsRouting" as the initiator, but it did not pass along the input parameters or any Forms data; adding the inputs manually didn't change anything either.

I imagine the complication is that Set works quite differently from Retrieve since it only runs at the end of a workflow, regardless of where it is in the diagram, and it needs an active/waiting instance whereas Retrieve can be used long after a BP instance has completed (i.e., Forms is waiting for a callback from the invoked workflow so it can receive any necessary data before moving to the next step and a child workflow is kind of outside that scope since it can reach the "completed" stage independently).

Based on that, it seems like the only way to do this at the moment would be to pass the data back up to the parent workflow so it can be done there.