Are you using a self-hosted TeamSpeak 6 server or a myTeamSpeak-hosted Community? Please also provide the exact server version, as well as the operating systems and TeamSpeak client versions used by both of you.
Perhaps the following steps from this existing topic will help you:
In that particular case, configuring the firewall to preserve the original UDP source ports resolved the problem. This does not necessarily mean that you have the same configuration issue, but it shows that an endless “Connecting…” state can be caused by NAT or firewall handling.
Please also try connecting one device through a different network, such as a mobile hotspot, and test it again. If it works through another network, the issue is most likely related to the original router, firewall, NAT configuration, or ISP interfering with the P2P/STUN connection.
TeamSpeak v6.0.0-beta5 will also add an option to configure a custom port range for screen-sharing sessions. This may help users whose current network configuration prevents the P2P connection from being established.