FME - Get parts of lines within polygons and transfer polygon ID to lines in result

I’ve got a set of polygons (my investigation areas – identified by IDs) and a set of lines that intersect these polygons.

My task is to only get the lines within the polygons and give them the containing polygon’s ID. I tried to do this with FME and used a Clipper, which gets the work done on the geometry part: It gives me the parts of the lines that are inside the polygons, but I don’t know how to transfer the said ID, which I need to sort and group the lines by in my result.