Weyl submodules in restrictions of simple modules

Let F be an algebraically closed field of characteristic p>0. Suppose that SLn−1(F) is naturally embedded into SLn(F) (either in the top left corner or in the bottom right corner). We prove that certain Weyl modules over SLn−1(F) can be embedded into the restriction L(ω)↓SLn−1(F), where L(ω) is a simple SLn(F)-module. This allows us to construct new primitive vectors in L(ω)↓SLn−1(F) from any primitive vectors in the corresponding Weyl modules. Some examples are given to show that this result actually works.