Enter a new proposed US-Mexico agreement that will synchronize, or "totalize" (a government finance term), the retirement programs of both countries. Among other things, it would allow full access to their benefits for Mexican employees working legally in the US who've paid into the US Social Security system.
From another one of your links:
It would bring Mexico in line with 20 other countries already covered under similar arrangements
But that's not what YOU said at all, is it?
You said ILLEGALS. And that's just not true.