Finite presentability of Bruck-Reilly extensions of Clifford monoids

Let M be a Clifford monoid and let θ be an endomorphism of M. We prove that if the Bruck–Reilly extension BR(M, θ) is finitely presented then M is finitely generated. This allows us to derive necessary and sufficient conditions for Bruck–Reilly extensions of Clifford monoids to be finitely presented