Can anyone tell me more about this flash hider and takedown tool?

[klaus 3338]

Found that in the "Ministerial- Blatt für die Preußische innere Verwaltung" with date of 23. Mai 1928: ....the hole of the muzzle protractor is to be enlarging to 9,07mm. Reason was that the muzzle protector as a part for cleaning the barrel molded the cleaning material on the cleaning rod. That was not helpful to clean the barrel.
Interesting is that only the muzzle protectors (as can be seen on the added pic) were enlarged. The Erma was not. That would mean that the Erma "muzzle protectors" were never used as it but were only used with the 4mm barrels.
The rifling of the Gomann barrels is different to the Erma barrels.