The one on the left is the spacer to make the cleaning rod and cleaning jag go only to the chamber mouth.
You slip the cleaning rod into it and use the small rod in the picture to go through the spacer and the cleaning rod both, forming a T handle.
I find it interesting that you have done so much modding of your Mosin, yet know so little about what you started with ...... spend some time reading at 7.62x54r.net ......
tobnpr:
You make an excellent point. The steel rod that comes with the gun is a nice piece of history but not a good choice for the care and feeding of the rifle.
Live well, be safe
Prof Young