You are right Robert, it looks very much like the SKS or AK style tubular cleaning kits.
I don’t own one of these so I can’t post a picture of it for comparence.
I do know that the SKS/AK tubular cleaning kits are smaller.
They are about as big as the screwdriver and brush that fit in the tube.
Here’s a poster of a Mosin Nagant and accoutrements that shows the tubular Mosin Nagant cleaning kit.
I borrowed this picture from the internet.
Got one myself at home.
I’ll post a close up picture of it this evening.
Should be later this afternoon on your side of the pond.
Met vriendelijke groet,
Martin