Diagonal reduction algebra for $\mathfrak{osp}(1|2)$

The problem of providing complete presentations of reduction algebras associated to a pair of Lie algebras $(\mathfrak{G},\mathfrak{g})$ has previously been considered by Khoroshkin and Ogievetsky in the case of the diagonal reduction algebra for $\mathfrak{gl}(n)$. In this paper, we consider the diagonal reduction algebra of the pair of Lie superalgebras $(\mathfrak{G},\mathfrak{g})$ as a double coset space having an associative $\scriptstyle\lozenge$-product and give a complete presentation in terms of generators and relations. We also provide a PBW basis for this reduction algebra along with Casimir-like elements and a subgroup of automorphisms.