Let the second author to go to the conference instead of the first author who also wants to go
You're going to get a lot of opinions on this, but I think that if the second author wants to go primarily for networking purposes, he should pay his own way. The student wants to go, did the majority of the work, and is the primary author of the paper. The fact that the student will leave academia after graduating is irrelevant. The student should have his travel paid and present the work at the conference.