A long straight neutral conductor carries a current l. Assume that all the free electrons in the conductor move with the same velocity v. A is a stationary observer while B is moving same velocity v parallel to the conductor
A and B both observe non- zero magnetic field
A and B both observe approximately the same current i.
A observes zero electric field while the electric field observed by B is non-zero
Both the observer will see the same current as the current signifies the amount of charge crossing a cross-sectional area per second, which is going to remain the same whether the observer is moving or stationary. Similarly, in a current carrying wire there is magnetic field present in its surrounding, therefore both the person will observe non zero magnetic field.