Path to formal methods
In the preface of his book “Mathematical Discovery, On Understanding, Learning, and Teaching Problems Solving” George Pólya writes:


  Solving problems is a practical art, like swimming, or skiing, or
  playing the piano: you can learn it only be imitation and practice.
  This book cannot offer you a magic key that opens all the doors and
  solves all the problems, but it offers you good examples for imitation
  and many opportunities for practice: if you wish to learn swimming you
  have to go into the water, and if you wish to become a problem solver
  you have to solve problems.


I think there is no short path, especially for reaching the state of writing papers. It requires practice, a lot of it.

Some pointers:

If “limited background in mathematics and the formal aspects” means “has never conceived a proof and written it down” then something like this might be a start.

If something on the Theoretical Computer Science Cheat Sheet makes the student feel uneasy, then a refresher course of the according branch of mathematics would be advisable.

There are many  sources for mathematical writing: The lecture notes of the 1978 Stanford University CS209 course perhaps. Or this article by Paul Halmos.