Pfthb

I have several user accounts in Office 365 tenant. Two of them are almost identical (have similar settings but different contact info and name).
I try to fetch information (such as all folders and items) in user's mailbox using GetFolder operation from EWS API that contains next body:

<?xml version="1.0" encoding="utf-8"?>
<soap:Envelope xmlns:soap="http://schemas.xmlsoap.org/soap/envelope/"
 xmlns:t="http://schemas.microsoft.com/exchange/services/2006/types">
 <soap:Header>
 <t:RequestServerVersion Version="Exchange2013"/>
 <t:ExchangeImpersonation>
 <t:ConnectingSID>
 <t:PrimarySmtpAddress>Name.Surname@mydomain.onmicrosoft.com</t:PrimarySmtpAddress>
 </t:ConnectingSID>
 </t:ExchangeImpersonation>
 </soap:Header>
 <soap:Body>
 <GetFolder xmlns="http://schemas.microsoft.com/exchange/services/2006/messages"
 xmlns:t="http://schemas.microsoft.com/exchange/services/2006/types">
 <FolderShape>
 <t:BaseShape>AllProperties</t:BaseShape>
 <t:AdditionalProperties> </t:AdditionalProperties>
 </FolderShape>
 <FolderIds>
 <t:DistinguishedFolderId Id="outbox"/>
 </FolderIds>
 </GetFolder>
 </soap:Body>
</soap:Envelope>

I can successfully get info for one of these two mailboxes but when an error reply with the next body:

<?xml version="1.0" encoding="utf-8"?>
<s:Envelope xmlns:s="http://schemas.xmlsoap.org/soap/envelope/">
 <s:Body>
 <s:Fault>
 <faultcode xmlns:a="http://schemas.microsoft.com/exchange/services/2006/types">a:ErrorNonPrimarySmtpAddress</faultcode>
 <faultstring xml:lang="en-US">The primary SMTP address must be specified when referencing a mailbox.</faultstring>
 <detail>
 <e:ResponseCode xmlns:e="http://schemas.microsoft.com/exchange/services/2006/errors">ErrorNonPrimarySmtpAddress</e:ResponseCode>
 <e:Message xmlns:e="http://schemas.microsoft.com/exchange/services/2006/errors">The primary SMTP address must be specified when referencing a mailbox.</e:Message>
 <t:MessageXml xmlns:t="http://schemas.microsoft.com/exchange/services/2006/types">
 <t:Value Name="Primary"/>
 </t:MessageXml>
 </detail>
 </s:Fault>
 </s:Body>
</s:Envelope>

Why do I get such ErrorNonPrimarySmtpAddress error response? What can be the problem when I fetch data in the mailbox of the second user?

You need to use the primary SMTP address - I doubt Name.Surname@mydomain.onmicrosoft.com is the primary address.

Open the address book in Outlook (Ctrl+Shift+B), open the user, switch to the "E-mail Addresses" tab, look for the address with the "SMTP:" prefix (note the caps).