I found this googling the exact same problem, and now that I found a (quite simple) way to get more codecs to show up and I want to share that for the next guy/gal: I have TeamViewer 9 on Windows 10 and even with installing K-Lite and ffdshow, as was mentioned here too, I could only extend the liste to a rather unusable ffdshow option (very large file size and quality issues). I uninstalled both TeamViewer 9 and the K-Lite Codec Pack and then FIRST re-installed the Mega K-Lite Codec Pack (don't know if it's necessary to use the complete version) and only afterwards I re-installed TeamViewer. (To be safe I rebooted the system after each step because, you know, Windows). With that order, TeamViewer apparently is able to recognize the installed codecs completely and other codecs finally showed up in the conversion options: So it is possible, I hope this helps although I have a very old version of TeamViewer. If the issue persists in newer versions, it should be possible there too.
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