If after knowing the correct facts the company is willing to keep the employee in employment then it is at the discretion of the company and there is nothing which can force the company to take any action (at least to my knowledge).
I thought employees' resume was company's internal matter. If false resume is sent to client and the client enters into a contract with the company based on the false resume and later learns that the resume was false then the client can cancel its contract with the company (under section 19 of the Indian Contract Act, 1872). But if even the client is willing to continue then there is nothing wrong about it.
You may try bringing the matter to the client's notice (I'd suggest to do that anonymously).
P.S: I'm afraid, the matter is now going squarely outside the scope of this forum and would prefer to have no more discussion on this subject.