H4 can be relinked to wife's H1 upon next visa application.
Next time when travel, use wife's H1 notice to get H4 visa. Now he won't need to do anything unless he wants to use H4 for other purposes.
Next time when travel, use wife's H1 notice to get H4 visa. Now he won't need to do anything unless he wants to use H4 for other purposes.