Examples of finite dimensional algebras which do not satisfy the derived Jordan--H\"older property

We construct a matrix algebra $\mathrm{\Lambda }(A,B)$ from two given finite dimensional elementary algebras $A$ and $B$ and give some sufficient conditions on $A$ and $B$ under which the derived Jordan–H"older property (DJHP) fails for $\mathrm{\Lambda }(A,B)$. This provides finite dimensional algebras of finite global dimension which do not satisfy DJHP.