Thanks, but exactly the last part “But you need to research how to change the email receiver.” was my questions ??
Anyway, I solved the problem by buying the addon “Profile Tabs”, created a new tab “Contact” and simply insert the CF7 shortcode there. The addon automatically changes the “To”-Email to the profile owners email in the background somehow. In the contact from should simply remain the “[_your_email]” in the “To”-field.