That depends on what theme you’re using. If you find out what template or function is producing the author page, you can add a link the user’s profile page using the function bp_core_get_user_domain( $user_id ). You’ll have to pass in the correct user ID, which should be used in the author page, too.
Your addition might look like <a href="<?php echo bp_core_get_user_domain( $user_id ); ?>">Visit User Profile</a>
Thank you for your reply. The theme which we using is Zeen (premium theme from envato). Author archive pages are probably just from wordpress. I dont know what do you mean with template/function. In the zeen theme folder we dont have author-archives.php or something like that.