True, but not part of Quantum Mechanics. The interchangeability of matter and energy is a consequence of the Special Theory of Relativity, which is not a Quantum Mechanical theory, and which predates Quantum Mechanics by about two decades.
True - special relativity predicts the equivalence of mass and energy, and it was formulated before quantum mechanics.
False - conversion of mass to energy and vice-versa is not part of quantum mechanics. The modern formulation of quantum mechanics, quantum field theory, requires matter/antimatter annihilation (mass converted to energy) and pair production (a process in which a sufficiently energetic photon is converted into a particle and an antiparticle - energy to mass conversion). Both are experimentally observed.
In practice, it's both Quantum Mechanics and Special Relativity. E.g.:
Why does a photon colliding with an atomic nucleus cause pair production?