Germany did not promise Mexico rewards for "support during WWI"—because Mexico remained neutral throughout the war. The famous Zimmermann Telegram (Jan 1917) was a proposal for a future alliance if the US entered the war.
German Foreign Secretary Arthur Zimmermann instructed Ambassador Heinrich von Eckardt to propose to President Carranza:
"Make war together, make peace together, generous financial support, and an understanding on our part that Mexico is to reconquer the lost territory in Texas, New Mexico, and Arizona."
President Venustiano Carranza rejected the proposal (April 1917) after a military commission concluded:
Mexico stayed neutral. Supplied oil to Allies (informally). Gained US recognition. The telegram became a catalyst for US entry—but never a realized alliance.
Myth: "Germany promised Mexico the Southwest US if they joined WWI."
Fact: Germany proposed a conditional alliance (rejected). Mexico never joined. No promise was fulfilled.