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Fountain and Gomes  have shown that any proper left ample semigroup embeds into a so-called W-product, which is a subsemigroup of a reverse semidirect product T⋉Y of a semilattice Y by a monoid T, where the action of T on Y is injective with images of the action being order ideals of Y . Proper left ample semigroups are proper left restriction, the latter forming a much wider class. The aim of this paper is to give necessary and sufficient conditions on a proper left restriction semigroup such that it embeds into a W-product. We also examine the complex relationship between W-products and semidirect products of the form Y⋊T .