First you need to enable the SharePoint 2013 library or list to accept messages from any sender.
To verify whether you have the correct settings, open library that should accept messages and navigate to Library/List > Settings > Incoming email settings.
Set Allow this document library to receive e-mail? to Yes and under E-mail security policy select Accept e-mail messages from any sender.
Incoming email settings should be the following:
You cannot receive messages sent to the SharePoint list or library from external senders because our servers are not configured to accept email from external servers due to security reasons. However, you may use the following workaround.
To configure mail delivery to a SharePoint list or library from external email addresses:
- Create a contact for this SharePoint document library in CONTROL PANEL, under Services > Company Contacts page. The contact should have the same email address as the mail-enabled library or list.
- Create a distribution list in CONTROL PANEL, on the Services > Distribution Lists page. The distribution list must have the email address that you will provide to your customers to send documents to.
- Make the created contact a member of this distribution list.
Example: the distribution list email address is email@example.com. The Company Contact firstname.lastname@example.org is the only member of this distribution list. To send a message to the document library, external users will send to email@example.com. The message will be forwarded to firstname.lastname@example.org and then appear in the document library.
When you have set this up, mail sent to this distribution list will be delivered to your SharePoint site.