SharePoint Online Invitation emails are not received

Most customers lead with Exchange first when looking to Office 365, but for those that move to SharePoint Online whilst leaving Exchange on-premise may also experience a situation where SharePoint Online Invitation emails are not received.

There is a known issue issue that may occur when messages such as a Sharing Invitation is send from SharePoint Online as the IP addresses which are sending the mail are sometimes classified as invalid as Microsoft have not added the necessary Sender Protection Framework (SPF) IP addresses.

There are the list of Outgoing IP Address Ranges used by SharePoint Online:

https://support.office.com/en-US/Article/SharePoint-Online-URLs-and-IP-Addresses-99b11563-c42d-4c20-87d2-502e66d62164?ui=en-US&rs=en-US&ad=US

You will have to ensure your on-premise Exchange accepts these IP addresses to prevent them being dropped for failing the SPF record check.