[Dovecot] MD5 to CRAM-MD5 password conversion?

We have a plethora of accounts for which we would like to enable CRAM-MD5 but their passwords are stored as MD5 hashes. Is there anything we can do? Can we take a linux MD5 hashed password (e.g. $1$fac330ee$wd6Tll...) and convert it to dovecot's CRAM-MD5 format (e.g. {CRAM-MD5}b3f297...)?

Thanks!