I don't know if there's another way to do it than this one:

• First make sure that the axis of your second bone is good:

• Create the animation for your first bone. Select the keyframes in the Dopesheet and copy, make sure to have the Only Selected (little arrow icon) option enabled:

• Select the second bone, in the Dopesheet create a keyframe on its rest position (this step seems necessary):

• Now paste in the DopeSheet, it creates new keyframe(s) the second bone has now the same animation as the first one:

I don't know if there's another way to do it than this one:

• First make sure that the axis of your second bone is good:

• Create the animation for your first bone. Select the keyframes in the Dopesheet and copy, make sure to have the Only Selected (little arrow icon) option enabled:

• Select the second bone, in the Dopesheet create a keyframe on its rest position (this step seems necessary):

• Now paste in the DopeSheet, it creates new keyframe(s), the second bone has now the same animation as the first one: