Office 365 e-mail being blocked by recipient security

We have recently migrated a customer to Office 365 from Exchange 2003. However, we have an issue with outbound e-mail being blocked by external recipients. Examples of NDR messages below.
1.      ukmx05.thermofisher.com
Remote Server returned '554 rejected due to spam content'
2.      barracudas.wikoff.com
Remote Server returned '554 rejected due to spam content'
3.      mx01.fivenines.co.uk
Remote Server returned '554 rejected due to spam content'
4.      host 149.255.60.65[149.255.60.65] said: 554
    rejected due to spam content (in reply to end of DATA command)
5.      [208.81.68.3] said: 554 Denied
    [CS] [29554e45.0.101986.00-2369.176968.s17p02m013.mxlogic.net] (Mode:
    normal) (in reply to end of DATA command)

Multiple users are being blocked randomly and regularly by different recipients. The customer is losing confidence. So we are keen to find a resolution as quickly as possible.

Any help would be gratefully appreciated.
swan_solutionsAsked:
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Vasil Michev (MVP)Commented:
Check if your domain has ended up in some blacklist. Check if your SPF record is correctly configured to include EO.

The NDR looks a lot like what Baracuda's are generating, so you should also ask the recipient side to whitelist your domain, and/or all EO ranges.
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