Which theory is being broken for the energy state to become 'forbidden'?
It's actually chemistry, not physics. Quantum chemistry. I completed a BSc course in chemistry and even planned of continuing in this particular specialisation. It was many years ago, but the above problem is quite basics.
OK, if it is undergrad level, surely there must be a book discussing the topic?
The posts are very wordy... why no equation?
I usually post equations, but I felt that you needed an intro - it is a good old (sadly forgotten) scientific tradition to acquire some culture before applying the method. My post is not "wordy" - these are keywords for your friend. He can now search them in books or online. I studied in Poland and the basic book was quantum chemistry by Prof. Kolos. It's possibly in the PhD curriculum at western unis.
No theory is being broken. Just the standard selection rules do not apply - one requires a more complicated model because of the presence of spin-orbit coupling (the consequence of the crystal symmetry). The transition momentum which would have null probability in the absence of the coupling becomes slightly non-zero due to this correction.
Could you explain the quantum mechanics required for the storage of this 'forbidden energy' in the phosphorescence of crystalline minerals please?
The question is awkward. "Forbidden energy" and "quantum mechanics required for its storage"? Commander Shepard in Mass Effect used more scientifically accurate language. Spin-orbit coupling causes phosphorescence in your colleagues case. There can be other effects which violate the simple selection rules and allow non-zero transition probability, though (e.g. many-body interactions or dipole moment of the investigated body/molecule).