Whilst they are in the MBAM quarantine they can't do any harm. However if you can copy them and send the samples to avast it would be good.
Unfortunately unlike avast it doesn't have an option to extract them to a temporary folder where you could zip, password protect and send the samples. The only option it gives is to delete or restore and with malware you don't want to restore to the original location it is too risky.
You could copy them from the quarantine folder, but I suspect that they would be encrypted as are those that avast puts in the chest, so they wouldn't be much use.
Without sample it is hard to add anything, but you should retain MBAM and do regular on-demand scans to act as a back-up to avast.