Not sure what you mean by engraving on the gun? I think you are asking if all police guns had unit markings; and the answer is no. I beleive that about 40% of police guns received unit markings, that is a feeling based on looking, owning and handeling hundreds of police lugers.
Many police lugers went into army service.
Your luger served in WW1, then at some point made it into police service recieving a sear and magazine safety and at some point the mag safety was removed.
It is hard to say if the grips are later armorer replacements or replacements by "someone".
Ed
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Edward Tinker
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Co-Author of Police Lugers - Co-Author of Simson Lugers
Author of Veteran Bring Backs Vol I, Vol II, Vol III and Vol IV
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