French entrenching tool captured from a German July 1916

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Could anyone please tell me what French unit this saw-back entrenching tool originally was issued to ?

It was taken from a German Infantry soldier in Mametz Wood, July 1916 and came with a standard German WW1 leather entrenching spade carrier.

It is made by "Goldenberg Acier Fondu" 1879 and has the "PGM" French military property marking used up until 1880. Basically this is the first/ original model of this tool used by the French

The French unit marking read;

13 677
25 L.I 53

The 25 and 53 have been crossed out.

Any help on which French units these markings relate to would be appreciated,

Chris

p.s. I found a bit information about this exact type of French entrenching tool on this Russian site; https://zhab.livejournal.com/676770.html?nojs=1
Attached Images

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French tool but German connection ???

I presume the Germans simply pressed these into service when they captured them during WW1 ???

The history is all engraved into the blade. Not allowed to show it all at this stage.

Plus an image of the unmarked German entrenching tool carrier which is showing real age, wear and tear,

Chris