You are talking about an external VPN (not Teamviewer's). So first connect to your external VPN, whatever that may be. THEN attempt the connection to your partner. I do not think that Teamviewer should be exitting when you turn on the VPN, but it is reasonable to lose its connection to the partner. This is because whenever you connect to a VPN two things happen: Everything that you send or receive is encrypted, and instead of going from You to your ISP to the Destination... it goes from You to your ISP to the VPN Server to the Destination.
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