According to the Tracker entry File System Repository files limited by PHP upload_max_filesize limits adding the capability Capabilities/moodle/course:ignorefilesizelimits to the Teacher role should allow users with this role to restore course backup files >system limit (in this case >128Mb). This is simply not the case. Users persistently get an error 'This file is bigger than the maximum size' when attempting to restore moodle2 course backups >128Mb. However, the site administrator can execute the restore. So there seems to be another capability which is also required. Anyone have an idea of which capability(s) these might be?
I sorted out the problem. I was attempting to restore a course with an account with the Manager role into a new course using Settings : Front page settings > Restore. I had set the capability ignorefilesizelimits for this role but when I checked the Front page permissions with Settings : Front page settings > Users > Permissions > Check permissions I found that indeed the capability ignorefilesizelimits did not include the Manager role. So I added this and, hey presto, Managers are now able to restore courses > 128Mb to new instances from Front Page restore.