Hi Ram,
There is not direct way to know which user approved the files on behalf of me. You can write custom reports to pull this data. Tables and field details are as below
Table :SRMWFPTHPS
Field : AGENT - Your user
Field : ACTAGENT - Approver who approved on behalf of you
This table is linked with key PATHID to table SCMG_T_CASE field WFPTHID.
From here CASE_GUID is linked with table /PSINDS/D_ATMSTR from which you can get the file numbers(PS_REFERENCE)
Regards,
Karthik