Back in 2013 a collector purchased at an Amoskeg auction a 1900 American Eagle Luger that was thought to be a preliminary sample of the U.S. Test Trials Luger. The gun was stamped with Ordinance “flaming bomb” markings and it had Ideal grips. The inside of the metal portion of the grips were also stamped with Ordnance bombs and “U.S. Property”, and the grips were numbered to the gun “5673”. There is no record of the serial numbers of any pre-trial test guns and there is no record of official purchase of Ideal grips and stock by the U.S. Army. Given the lack of documentation or other provenance, the authenticity of any “U.S. Property/flaming bomb” Ideal grips and stock falls somewhere on the continuum of “unknown->unlikely->dubious->fake”, and in light of no recorded verification I am inclined to opt for “dubious” at best.
In the unlikely event that there is some veracity to the association of the Ideal stock/holster to official U.S. Army acquisition it would seem that the stock you have numbered “5600“ is precariously close to the serial number of the aforementioned 1900 AE Luger and grips and possibly all have the same origin, official or unofficial. It might be neat to have them all together.
Looking forward to your photos!
Ron