The future employer shoud NOT contact

your current employer if you are employed. Even though they could with your permission. It is PERFECTLY FINE to disallow them to contact your current employer.

However if you are not employed, you should allow them to check, otherwise it can raise some red flag.

The background check can take up to 2 weeks, so just be patient since your have passed the hard part. You should do follow up in one week for status update and provide new documentation as needed to speed up the process.

Congratulations for your new job and enjoy your weekend.