German officials had to know the absolute hopelessness of a Mexican invasion of the U.S...seems they had little to gain other than further than U.S. combat troops in Europe. However, the war was shortened by at least a year with direct U.S involvement, the main benefactors being France and Great Britain of course. Not sure how this sub feels about conspiracies, any thoughts?
Any attempt to suggest that the Zimmerman telegram was a fraud on the part of the British or their allies is rather fatally undermined by the fact that Zimmerman himself publicly admitted it was an authentic message after the decoded version of the telegram was released by the US.
With regard to what the Germans hoped to achieve by involving Mexico in a war with America, it's important to bear in mind that at the time the telegram was sent (January 1917), the country was by no means on a war footing and the US Army was still a relatively small, professional force. The diversion of this force to fight a war with Mexico could have been a significant - if only short term - impediment to military planning for a war in Europe.