Undeliverable Mail

Hello,

We're using Microsoft Office 365 Online.

One of our user who is trying to send mail to a client but the user is getting Undeliverable failure mail, I could not conclude whether this is Microsoft Exchange 365 with DNS problem or with the client's domain, below is the failure information, please help me to identify as to what I must proceed with.

From: MAILER-DAEMON@MAILER-DAEMON [mailto:MAILER-DAEMON@MAILER-DAEMON]

 Sent: Monday, January 07, 2013 11:49 AM

 To: sourceuser@apppoint.com

 Subject: Undeliverable: Mail Subject.

 Delivery has failed to these recipients or groups:

 client1@teamhjs.commailto:client1@teamhjs.com

A problem occurred and this message couldn't be delivered. Check to be sure the e-mail address is correct. If the problem continues, please contact your helpdesk.
Diagnostic information for administrators:

Generating server: bigfish.com

client1@teamhjs.com

 #554 5.4.4 SMTPSEND.DNS.NonExistentDomain; nonexistent domain ##

Original message headers:

Received: from mail148-ch1-R.bigfish.com (10.43.68.226) by CH1EHSOBE006.bigfish.com (10.43.70.56) with Microsoft SMTP Server id 14.1.225.23; Mon, 7 Jan 2013 06:18:29 +0000

Received: from mail148-ch1 (localhost [127.0.0.1])      by

 mail148-ch1-R.bigfish.com (Postfix) with ESMTP id C9C643401F0  for <client1@teamhjs.com>; Mon,  7 Jan 2013 06:18:29 +0000 (UTC)

X-Forefront-Antispam-Report:

CIP:111.221.116.197;KIP:(null);UIP:(null);IPV:NLI;H:SIXPRD0610HT001.apcprd06

.prod.outlook.com;RD:none;EFVD:NLI

X-SpamScore: 9

X-BigFish:

PS9(z1346pzc89bhc85dhzz1de0h1202h1e76h1d1ah1d2ahzz8275bh8275dh1730fah177df4h

18c673h1954cbh17326ahz32i2a8h668h839hd24he5bhf0ah1249h1288h12a5h12bdh137ah13

9eh1441h1504h1537h162dh1631h1758h17f1h1155h)

Received: from mail148-ch1 (localhost.localdomain [127.0.0.1]) by

mail148-ch1

 (MessageSwitch) id 135753950750722_12531; Mon,  7 Jan 2013 06:18:27 +0000

 (UTC)

Received: from CH1EHSMHS027.bigfish.com

(snatpool1.int.messaging.microsoft.com

 [10.43.68.247])        by mail148-ch1.bigfish.com (Postfix) with ESMTP id

 F2B79300094    for <client1@teamhjs.com>; Mon,  7 Jan 2013 06:18:26

+0000

 (UTC)

Received: from SIXPRD0610HT001.apcprd06.prod.outlook.com (111.221.116.197) by  CH1EHSMHS027.bigfish.com (10.43.70.27) with Microsoft SMTP Server (TLS) id  14.1.225.23; Mon, 7 Jan 2013 06:18:26 +0000