You need to allow relaying by adding an SPF record.
Setting up SPF Record Inclusion
Add an SPF DNS record allowing mail to be sent, if the outgoing mail is purporting to be from your domain e.g. [email protected].
SMTP servers often reject mail which pretends to be from that domain if it originates from another SMTP server outside of that domain.
The SPF record tells the SMTP server for that domain that theaccessgroup.smtp.com is OK to send mail on behalf of COMPANY.com.
The format of the SPF record is as follows: v=spf1 include:spf2.accessacloud.com -all
Also add an external relay receive connector to their exchange server allowing mail originating from theaccessgroup.smtp.com into your domain.