I think "usurp" captures the idea here; Evita had done what they had been trying to do, and had thereby robbed them of the satisfaction of achieving it themselves. You might say "was usurping a historical claim and a longed-for victory which were rightfully theirs"; I think the last part would express the implications of "les arrebataba". Alternatively you could just say "was usurping their historical claim and longed-for victory".

"Rob" could be used too: "was robbing them of a historical claim and a longed-for victory".

Alternatively, instead of "historical", you could say "a longstanding claim", but I think I would use "historical", which makes it seem more important and more a matter of human rights.

It's often difficult to find the right word for "reivindicación". I think "claim" is probably best here; the idea is of claiming a right. "Demand" could also be used.