They exchanged part on a regular basis but only when they didn't have their own parts available. I suspect, some of the very early Savages would have had the Long Branch "button" cocking piece, because Long Branch had a bunch left over and Savage either hadn't started producing them yet or was in short supply. The same went for most small parts, magazines, barrels, bands and furniture. When the Savage contract was cancelled in late 1944, all of the equipment and parts were shipped to Long Branch.
It doesn't take much thought to realise that during war time production and many expediencies that if different plants were making identical firearms, with interchangeable parts that they would share parts between the two of them, rather than shut down the production lines for lack of in house produced parts.
I just found out my old aunt, worked at Long Branch from 1943-1944. One of her jobs, was to unpack stock parts and take them to the assembly areas. She mentioned that she didn't like it when they received parts from the US, because they were heavier than the parts from Canada. It seems that her jobs changed quite a bit. The attrition rate there was pretty bad. Not because of working conditions but because of the life styles required to work there. My aunt, came off an Alberta farm at 17 years old and went directly into a full out factory environment where quality and speed were the bywords of the day. Many couldn't keep up with the pace and many also only came for the good wages to pay off bills or go to school etc. She said there was as much overtime as they wanted to work. She really liked it. She has a picture of herself and two other girls from Beiseker, Alberta that went there together after applying for the jobs out of an ad in a local newspaper. The train fare there, was taken off their pay. She laughed and said that there wasn't any work in Alberta so none of them minded. She was overwhelmed by how many people were there and what Long Branch did to keep them there. They created a small city around the factory site and provided all kinds of social events. I'm getting off topic, I apologise.