General steps:
1) Activate admin menu access add-on.
2) Go to ‘Users->User Role Editor’, select ‘administrator’ role.
3) Click ‘Admin menu’ button and find menus related to a ‘property listing’ plugin, check what capabilities are required for them (3rd column).
4) Select a role, under which your user will work. Grant those capabilities to this role. Look at admin menu. Block unneeded menu items if you find some.

You can send me (support [at-sign] role-editor.com) a copy of “property listing manager” plugin (via dropbox or similar) and I will explain you what to do with it.

Or send admin login credentials. I can look at it on-line then.