Is this legal for a private pilot?

I'm an instrument rated private pilot. My CFI was going to fly with
one of his student pilots to an airport an hour away to go to the
student's vacation home, providing instruction along the way. Then he
would leave the student there for a couple days, and return to pick the
student up.

Now the CFI can't make it and wants to know if I will make the trip
instead. I would pay for half the flight expenses and of course be PIC
for both flights. Is this legal?