You can easily know which SAP transport request has been imported to a system. Go to transaction SE16 -> E070 2, Fill the input criteria and execute 3. You will see the transport requests number have been imported.
In some cases you want to know who imported transport request to a system. You can check from Table TPLOG that gives you the information. Execute transaction SE16 –> TPLOG. Filter the date you want. Enter “IMPORT*” at field Text. You will know the users who did transport.