  We analyze, using first-principles calculations and the method of invariants,
the spin-orbit proximity effects in trilayer heterostructures comprising
phosphorene and encapsulating WSe$_2$ monolayers. We focus on four different
configurations, in which the top/bottom WSe$_2$ monolayer is twisted by 0 or 60
degrees with respect to phosphorene, and analyze the spin splitting of
phosphorene hole bands around the $\Gamma$ point. Our results show that the
spin texture of phosphorene hole bands can be dramatically modified by
different encapsulations of phosphorene monolayer. For a symmetrically
encapsulated phosphorene, the momentum-dependent spin-orbit field has the
out-of-plane component only, simulating the spin texture of phosphorene-like
group-IV monochalcogenide ferroelectrics. Furthermore, we reveal that the
direction of the out-of-plane spin-orbit field can be controlled by switching
the twist angle from 0 to 60 degrees. Finally, we show that the spin texture in
asymmetrically encapsulated phosphorene has the dominant in-plane component of
the spin-orbit field, comparable to the Rashba effect in phosphorene with an
applied sizable external electric field. Our results confirm that the
significant modification and control of the spin texture is possible in low
common-symmetry heterostructures, paving the way for using different substrates
to modify spin properties in materials important for spintronics.
