Male threads cut on the barrel - corresponding female threads on the false muzzle. The trick was threading the muzzle so that it indexed with the front sight dovetail aligned with the rear sight. First try it slightly over indexed - a light preening applied to the face of the muzzle allowed a slight under index that tightened snugly at index. Red loctite was also applied to the threads.
My friend gets all the credit for the workmanship. He is a retired history professor who sportered many dozens of mausers into high quality hunting rifles over the years. He has accumulated a myriad of military surplus parts over the years. So in a strange twist of fate he now finds himself enjoying restoration projects and assisting aspiring collectors like myself restore the same rifles he dismembered in his former life. He only sporters previously "bubbaed" rifles today. He almost never will accept payment - I have to find creative ways of repaying him - like the extra m1917 handguard I bought for him to complete his Winchester m1917 restoration. Being a history professor he also can communicate a wealth of history regarding these old weapons.