Can he sign his form 16 ?

yes, he can sign in his form 16 also, because the person authorised in the TDS return can sign in the form 16.

Agree with Ashok. Yes Sr. Manager Finance can sign his own form 16 since he is authorised to sign the TDS Returns.

I think there must a BOD Resolution authorising the Sr. Manager Finance to sign Form 16, 16A, TDS Returns etc.

AGREE WITH MR. ASHOK YES, SR. MANAGER FINANCE IS SIGN HIS FORM 16 SINCE HE IS AUTHORIES TO SIGN THE TDS RETURNS OF THE COMPANY