Spin conservation in circuits with a spin filter

Since you want to influence the spin of the electrons by a magnetic field, why don't we talk about the magnetic dipole of the electrons instead of their spin. At least both are connected by their alignment; under the influence of a magnetic field they get aligned with this field.

The next effect is the acting Lorentz force, in your case better called the Hall effect. The difference lies in the movement of the conductor with its electrons (Lorentz force) against the displacement of the electrons within an immovable conductor. However, in regions behind the magnetic field the forced alignment is lost immediately.

I can only think of one exception. The conductor behind the magnetic conductor is influenced by the incoming spin-polarised electrons to such an extent that its electrons align themselves with the incoming electrons and the magnetic field generated increases to such an extent that self-inductance (self-maintaining of the field) occurs. We obtain a magnetised material. Then the electrical resistance actually increases.