We analyze, using first-principles calculations and the method of invariants, the spin-orbit proximity effects in trilayer heterostructures comprising phosphorene and encapsulating WSe2 monolayers. We focus on four different configurations, in which the top/bottom WSe2 monolayer is twisted by 0 or 60 degrees with respect to phosphorene and analyze the spin-splitting of phosphorene hole bands around the 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 phosphorenelike 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.