The finite basis problem for the endomorphism semirings of finite semilattices

For every semilattice $\mathcal{A}=(A,+)$, the set $\mathrm{E}\mathrm{n}\mathrm{d}(\mathcal{A})$ of its endomorphisms forms a semiring under pointwise addition and composition. We prove that that if $\mathcal{A}$ is finite, then the endomorphism semiring $\mathrm{E}\mathrm{n}\mathrm{d}(\mathcal{A})$ has a finite identity basis if and only if $\mathrm{\mid }A\mathrm{\mid }\le 2$.