From wplms s3 version 1.6 ,plupload option is available to upload files larger than your upload limit to amazon s3 .
1. Enable plupload from wp-admin -> lms -> settings -> wplms s3 and set maximum upload file size
2. Now you will see change in ui of upload to Amazon s3 .Just select the files :
NOTE : BIG files may take time to upload so please be patient and do not close the window until process is completed .