Embedding a graded matrix algebra into an elementary graded

M.V. Zaicev and S.K. Segal, as well as S. D\u{a}sc\u{a}lescu, B. Ion, C. N\u{a}st\u{a}sescu, and D. Raios Montes studied certain gradings on matrix rings and algebras - ‘elementary’ gradings. However, examples of gradings on a matrix ring that are not elementary are known. In the present article, we show that any subalgebra of a full matrix ring over an arbitrary graded division ring can be embedded in an elementary graded matrix ring.