You should contact your license authority ( state of issue) as you must now comply with PART FCL to get the EASA conversion. The issuing state will also need your medical records and thus you will need an EASA Part MED compliant certificate. If your 777 type rating was completed outside the EU you may be asked for a copy of the training records/ program. The Examiner that signed the LPC must also be approved by the EASA state. All acceptable means of compliance can be found on EASA website but you should get the exact requirements from your authority. Under EASA you may only have one " state of licence issue" so not sure how that will work if you are flying on a QR licence unless you are maybe flying on your JAR licence with " validation" from QR.