The source that I read had some of the history of the Austro-Hungarian use of the Mosin as well.
They captured a lot and were given more by the Germans.
The first several thousand were bored (and I imagine re-rifled) and rechambered in 8x50r Mannlicher, the cases being identical length to the junction of shoulder and neck and slightly larger in diameter with the rims being similar enough to work.
Then testing showed that the Mosin was strong enough to fire the 8mm projectile without reboring

, so they were just rechambered after that, and the throat lengthened to allow for the longer projectiles.
It was these ones that had the chamber inserts put in by SAKO, and they were brazed in from all that I could find then chambered for 7.62x54r.