H-4

H-4 extension

If you are on H-1 and transferred, your spouse doesn't need to transfer H-4. As long as the visa/I-94 is valid, you are in good shape. However, when visa/I-94 expires, you need to file for I-539 - Application to Extend/Change non immigrant status.

Fee for this is $300, attorney fee would be $350. You can fill it yourself and send it to USCIS, no need of attorney.

Make sure that you file for this at least a few months before expiry.