The Use of the term “JNFANTERIE GEWEHR” ( with the “J”) would indicate use in the M1888 Rifle and Carbine (Kar 88) with an adaptor ( probably steel) made like the M88 RN Cartridge.
5,44mm would be a .214 Bore with rifling at about .220 Grooves): designed not to be able to use the common .22RF ( 5,6 Flobert). ( ICBW, the “5,44” could be a commercial CALIBRE, then the BORE would be around 5,2mm ( used in Mondaragon experimentals) or .205". which ever it is, it is a “One off” size.
A Bullet this small would be able to have an adaptor “barrel” extending up the cylindrical “8mm” Bullet as well, probably with a modicum of Rifling. Generally made for “Indoor Barracks Practice” during the colder winter months, which in Northern and Eastern Germany was very cold indeed.
Interesting. Now to find a matching steel adaptor.