With Office 365, it is possible to invite external people to access your private SharePoint collections.

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However, this feature is not enable by default.

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So, to enable this feature, there are few actions to do.

First, connect to the SharePoint Administration portal (https://yourdomain-admin.sharepoint.com) and go to the Site Collection Management

Select the site collection on which you want to allow external user invitation and click on the Manage Share by Email button

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Click on the Enable option

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Then connect to your site collection and go to the Site Settings

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Then click on the Site collection features link

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Enable the feature External user invitations

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Finally, open the Site Actions menu and click on Share Site

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Enter external user email addresses on the field associated with the right level to provide to external user

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A confirmation is shown if email invitation has been sent successfully

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External user receive the invitation to access your SharePoint site

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Once external user has accepted the invitation, it appears on the People and Groups list and no license has been consumed