Hi Antonio,
Checking Webster, I find that the following rifles went to Argentina, not Peru:
1899 53,000 (all of) O5000-T7999
1900-1901 16,000 (half of) T8000-W9999
(page 109)
So my Argentine rifle K4875 is in Argentine stock T5446. That solves that question.
Page 125 says Peru got 16,000 rifles and bayonets, with half the rifles from unassembled lots. They were to have been from the U, V, and W blocks which had been shipped to Buenos Aires. They were returned to Germany where the Argentine crest was removed and the Peruvian crest applied. Plans were modified at some point because some R and S block rifles have been found with Peruvian crests. All rifles had the flat sight; Preuvian rifles had the sight replaced by the Lange sight in 1912 for spitzer ammo. Argentina's deal with DWM was that Argentine involvement in the Peruvian contract was to be kept secret.
Of course there were still a few earlier Argentine rifles that somehow found themselves in Peru. I think we can say that any M1891 rifle with an Argentine crest found in Peru is one of this group of 'strangers', not a part of the 16,000 contract rifles, all of which had Peruvian crests. These 'strangers' would have first been in Argentina and later in Peru.
Regards,
Bill