Answer
No. Yes.
Work Step by Step
The two inertial observers measure different velocities for the truck at any given time, so their reports on the truck’s momentum vector, $m\vec{v}$, will differ by a constant amount.
However, though the velocity measurements differ by a constant amount, the change in velocity between any two times will be the same as reported by the two observers (because the “constant amount” cancels out), and so will the rate of change of momentum.
