If you find that a spoofed email is reaching users inboxes in Microsoft 365 (say something like managing.director@gmail.com pretending to be managing.director@yourdomain.com) then here are some initial suggestions and things to check.

Firstly, ensure you have SPF, DKIM DMARC configured for your domain. They all help reduce spoofed emails getting to the inbox. 

Set up SPF to help prevent spoofing

Support for validation of DKIM signed messages

Use DMARC to validate email

Next, run the analyzer that is built into the Microsoft 365 Security Center to see where your policies may deviate from best practices.

Configuration analyzer for protection policies in EOP and Microsoft Defender for Office 365

and you’ll find those best practice settings here:

Recommended settings for EOP and Microsoft Defender for Office 365 security

I’d be checking against the strict rather than the standard settings if it was me.

In the settings for your spam policy in Exchange Online there are a few additional settings you can enable as shown above. Even though the Microsoft best practices doesn’t recommend it, I still have most of these set and at a minimum recommend that the SPF hard fail option be enabled.

In your Anti-phishing policies ensure the option for Show first contact safety tip is enabled as shown above. Microsoft Best Practice policies don’t set this. In general make sure all the above settings are all enabled as shown.

Another good indicator to configure is

Set-ExternalInOutlook -Enabled $true

using PowerShell, that will let you know about

Native external sender callouts on email in Outlook

Another custom adjustment you can consider is changing the Spam Confidence Level (SCL)

Spam Confidence level (SCL) in EOP

A further option you may wish to tweak beyond Microsoft’s recommended best practices is the phishing thresholds in anti-phishing policies:

Advanced phishing thresholds in anti-phishing policies in Microsoft Defender for Office 365 

When you get emails that are confirmed as trying to trick users, make sure you report them to Microsoft

How do I report a suspicious email or file to Microsoft?

Use the Submissions portal to submit suspected spam, phish, URLs, legitimate email getting blocked, and email attachments to Microsoft

Probably the best way to do that is to use the free add-in that works with Outlook.

Enable the Report Message or the Report Phishing add-ins

doing so helps build the intelligence for Exchange Online as well as helping others who may see similar insecure emails.

The final option available to you is always to reach out to Microsoft for assistance.

Get help or support for Microsoft 365 for business

I would also suggest you check any white listing options you may have in Exchange Online as these are easily forgotten over time. Best practice is not to white list any domain or specific email address but always check when you see repeated emails get through filtering. I can’t tell you how many times I find this as the cause of any issue. Keep in mind, there are few places that you can white list emails:

Create safe sender lists in EOP

You can of course also block the insecure sender:

Create blocked sender lists in EOP

Remember that if you tighten your email security the result will probably be an increase in false positives, at least initially, as Exchange Online learns to evaluate the changes and user behaviours based on the updated settings. Email security is not an exact science. The bad operators are working just as hard to bypass all these settings so it is always going to be a game of cat and mouse. However, hopefully, using the Microsoft recommended best practices and some additional tweaks as suggested above, you can prevent the vast majority of insecure emails out of your users email boxes.