I always try to offer alternatives before advocating the use of our tools, so let's discuss some options. As
@edossantos mentioned, the current server-side integration does not deal with voicemails, so you will have to handle them yourself.
Voicemails are nothing more than a .wav file (with a matching .xml file). So uploading them to your CRM is certainly possible. As a programmer you can create a filesystemwatcher that detects a new voicemail and then takes an action. 3CX waits to write these files to disk until the call has ended, so you can process them right away. That's what we do with our
3CX Voicemail Manager tool.
Voicemails are organized on disk in folders matching the extension number (C:\ProgramData\3CX\Instance1\Data\Ivr\Voicemail\Extensions), so it is easy to identify who owns the voicemail file. Embedded in the voicemail file name is useful information about who the voicemail was from (phone number). As a result, you should be able to easily match the voicemail to a contact in your CRM. Hopefully that's enough information to help you get started if you want to try to handle this yourself.
I do encourage you to take a look at our
3CX Voicemail Manager tool. Our tool makes it easy for managers to monitor voicemails and add introductions to the voicemail before forwarding to a colleague. In addition, we have enhanced group voicemail that turns on the MWI for group members, and turns it off when anyone in the group listens to the voicemail. We also have time-based voicemail escalation to ensure voicemails do not go unheard for too long. We can help you with voicemail management. I have only scratched the surface of what we can do.
Finally, If you want to build a CRM integration with support for voicemail processing, there are options in addition to the server-side integration. 3CX has announced a new REST API scheduled for release later this year. And a new Gateway service. We do not know what capabilities these new tools will offer, but you may have more options soon. Until then, we (VoIPTools) have both a REST based API (for managing 3CX files for example), and an "events" API so you can be notified of a new voicemail. With a little effort, you can do just about anything.