If you want an external project member to be able to invite their own company employees or another external member to your project, proceed as follows:
1) Log in under the web app in your account.
2) In the project overview, select the corresponding project and click on the the "Members" section at the top right of the relevant project to view the members members invited so far.
3) Now click on the name of the external project member (easy to recognise, as the addition "Project admin" is not shown here)
4) Once here, please click on the pencil icon under the "Role" section next to "Member".
5) In the menu that opens, select the "Project admin" entry.
The external project member has just been assigned the new role.