So it won’t stick then, even though they’ve signed it?
Not necessarily. The key point that cycni-al is making is that a manifest error generally makes a contract non-binding to that extent.
In other words, should you come to the end of the period of months that you both reasonably thought you had agreed as the end point and then tried to rely on the agreement as binding for another 18 months, then you might find yourself in a difficult position.
As it is, of course, there may become some additional funding available (on this or another grant) that does actually mean you can stay on. I can’t profess to fully understand the way that people’s jobs are funded in Universities (Dr North is forever being funded by 10% here, and 20% there on grants).