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Try below from EMS<br />
<br />
get-mailpublicfolder &quot;test@mydomain.com&quot; | get-publicfolder
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when I ran your command it returns me an error below<br />
The operation couldn't be performed because object 'test@mydomain.com' couldn't be found on 'dccontroller.mydomain.com<wbr />'.<br />
&nbsp; &nbsp; + CategoryInfo &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;: NotSpecified: (:) [Get-MailPublicFolder], ManagementObjectNotFoundEx<wbr />ception<br />
&nbsp; &nbsp; + FullyQualifiedErrorId : [Server=EXCH2016,RequestId<wbr />=2f671dbd-<wbr />6436-47ab-<wbr />a16e-06255<wbr />04a6300,Ti<wbr />meStamp=12<wbr />/10/2019 1<br />
&nbsp; &nbsp;:37:05 PM] [FailureCategory=Cmdlet-Ma<wbr />nagementOb<wbr />jectNotFou<wbr />ndExceptio<wbr />n] CC36F1DC,Microsoft.Exchang<wbr />e.Manageme<wbr />nt.MapiT<br />
&nbsp; asks.GetMailPublicFolder<br />
&nbsp; &nbsp; + PSComputerName &nbsp; &nbsp; &nbsp; &nbsp;: exch2016.mydomain.com<br />
<br />
what is the syntax to check shared mailbox for such address?
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leop1212

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I have an object in my exchange 2016 on premise server with email address test@mydomain.com <br />
could you provide a cyntax on how I can find which object has this email address assigned -test@mydomain.com ?
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I have an object in my exchange 2016 on premise server with email address test@mydomain.com 
could you provide a cyntax on how I can find which object has this email address assigned -test@mydomain.com ?

Try below from EMS

get-mailpublicfolder &quot;test@mydomain.com&quot; | get-publicfolder

when I ran your command it returns me an error below
The operation couldn&#39;t be performed because object &#39;test@mydomain.com&#39; couldn&#39;t be found on &#39;dccontroller.mydomain.com&#39;.
    + CategoryInfo          : NotSpecified: (:) [Get-MailPublicFolder], ManagementObjectNotFoundException
    + FullyQualifiedErrorId : [Server=EXCH2016,RequestId=2f671dbd-6436-47ab-a16e-0625504a6300,TimeStamp=12/10/2019 1
   :37:05 PM] [FailureCategory=Cmdlet-ManagementObjectNotFoundException] CC36F1DC,Microsoft.Exchange.Management.MapiT
  asks.GetMailPublicFolder
    + PSComputerName        : exch2016.mydomain.com

what is the syntax to check shared mailbox for such address?

How to find mail enabled  public folder or a mailbox with an with a certain email address?

Exchange is the server side of a collaborative application product that is part of the Microsoft Server infrastructure. Exchange's major features include email, calendaring, contacts and tasks, support for mobile and web-based access to information, and support for data storage.