Does SSN Card need to be changed after EAD?

dazzling

Registered Users (C)
Question: My spouse is working on H1B. We have received our EADs. She is now planning to start work on EAD with a new Employer. Does she need to re-apply for her SSN (to get the phrase - valid with INS authorization removed). Logically speaking even EAD is a temporary document (like H1B) and this should not be required. Just asking if someone has been in this situation. Thanks for your replies!!

Clarification: I am the primary applicant for our GC and I continue to work on H1B.
 
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