Should I submit all materials just like the original application, or I only need to mail the EAD with I-765 to USCIS?
-No, but provide the EAD approval notice (the piece of paper which the EAD was inserted) and original wrong EAD with the completed I-765. In the I-765:"I am applying for.." part, check/choose "Replacement..." and then, write a cover letter to address what is wrong in the EAD and ask the replacement of the EAD. You need to get the replacement which will have the validity duration to cover your current employment dates (you can work legally during the repalcement pending). If you apply for a new EAD, you can not work at present.
You need to make a photocpy of your wrong EAD and the EAD approval notice and keep it in your personal record. Show the wrong EAD and approval notice to your HR and explain it before you send them back to USCIS for repalcement.