Why not move over to SLACK, TEAMS or HIPCHAT ?
Microsoft has announced already that Skype isn't the future anymore.
Also SLACK - TEAMs offer more than Skype now.
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Have a look at https://marketplace.atlassian.com/apps/1212689/lync-and-skype-connector-for-jira?hosting=server&tab=overview
I have not tested this personally but it claims to do what you described.
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