NDR - What is causing this error

I have received the following NDR when replying to an email. It is the first time I have communicated with this person via email.

I am using Office 365.

Can someone explain how I might resolve this issue?

************************************************************************
Delivery has failed to these recipients or groups:
Nigel Davis
Your message was rejected by the recipient email server. Please check the recipient's email address and try resending your message, or contact the recipient directly. For more tips to help resolve this issue, see DSN code 5.1.0 in Exchange Online - Office 365. If the problem continues, contact your email admin.





Diagnostic information for administrators:
Generating server: DBXPR03MB144.eurprd03.prod.outlook.com
them@theirdomain.com
Remote Server returned '< #5.1.10 smtp;550 5.1.10 RESOLVER.ADR.RecipientNotFound; Recipient not found by SMTP address lookup>'
Original message headers:
Received: from DB3PR03CA0045.eurprd03.prod.outlook.com (10.255.183.45) by
 DBXPR03MB144.eurprd03.prod.outlook.com (10.242.141.23) with Microsoft SMTP
 Server (TLS) id 15.1.75.20; Sun, 1 Feb 2015 10:49:58 +0000
Received: from AM1FFO11FD030.protection.gbl (2a01:111:f400:7e00::185) by
 DB3PR03CA0045.outlook.office365.com (2a01:111:e400:9438::45) with Microsoft
 SMTP Server (TLS) id 15.1.75.20 via Frontend Transport; Sun, 1 Feb 2015
 10:49:58 +0000
Received: from emea01-am1-obe.outbound.protection.outlook.com (157.56.112.144)
 by AM1FFO11FD030.mail.protection.outlook.com (10.174.64.219) with Microsoft
 SMTP Server (TLS) id 15.1.75.11 via Frontend Transport; Sun, 1 Feb 2015
 10:49:58 +0000
Received: from AMSPR04MB423.eurprd04.prod.outlook.com (10.242.107.150) by
 AMSPR04MB422.eurprd04.prod.outlook.com (10.242.107.149) with Microsoft SMTP
 Server (TLS) id 15.1.65.19; Sun, 1 Feb 2015 10:49:57 +0000
Received: from AMSPR04MB423.eurprd04.prod.outlook.com ([10.242.107.150]) by
 AMSPR04MB423.eurprd04.prod.outlook.com ([10.242.107.150]) with mapi id
 15.01.0065.013; Sun, 1 Feb 2015 10:49:57 +0000
From: ed smith <me@mydomain.co.uk>
To: Nigel Davis <them@theirdomain.com>
Subject: RE: 121/Exhibitions
Thread-Topic: 121/Exhibitions
Thread-Index: AdA6PTJ8ZyvOp40+Tkud/295qdU2zADzrX+A
Date: Sun, 1 Feb 2015 10:49:56 +0000
Message-ID: <AMSPR04MB42366AB74EC83FB06957901993F0@AMSPR04MB423.eurprd04.prod.outlook.com>
References: <64ED5D0305730E4D889B7C43766769EB028F9CD23A33@N3-SRV-01.n3displaygraphi.local>
In-Reply-To: <64ED5D0305730E4D889B7C43766769EB028F9CD23A33@N3-SRV-01.n3displaygraphi.local>
Accept-Language: en-GB, en-US
Content-Language: en-US
X-MS-Has-Attach: yes
X-MS-TNEF-Correlator:
x-originating-ip: [86.174.132.242]
authentication-results: theirdomain.com; dkim=none (message not signed)
 header.d=none;theirdomain.com; dkim=none (message not signed)
 header.d=none;theirdomain.com; dmarc=permerror action=none
 header.from=mydomain.co.uk;
x-microsoft-antispam: BCL:0;PCL:0;RULEID:;SRVR:AMSPR04MB422;UriScan:;
x-exchange-antispam-report-test: UriScan:;
x-exchange-antispam-report-cfa-test: BCL:0;PCL:0;RULEID:;SRVR:AMSPR04MB422;
x-forefront-prvs: 04740D25F1
X-Forefront-Antispam-Report-Untrusted: SFV:NSPM;SFS:(10019020)(209900001)(51914003)(40134004)(99936001)(19617315012)(16799955002)(40100003)(54356999)(54606007)(54206007)(2656002)(15188155005)(19618635001)(77156002)(450100001)(33656002)(19627595001)(92566002)(19625215002)(86362001)(122556002)(62966003)(87936001)(19580395003)(50986999)(76176999)(19300405004)(110136001)(107886001)(74482002)(46102003)(66066001)(17760045003)(2950100001)(2900100001)(15975445007)(74316001)(77096005)(102836002)(86152002)(19580405001)(16236675004)(76576001)(15395725005)(18206015028)(15398625002)(15669805003);DIR:OUT;SFP:1102;SCL:1;SRVR:AMSPR04MB422;H:AMSPR04MB423.eurprd04.prod.outlook.com;FPR:;SPF:None;MLV:sfv;LANG:en;
Content-Type: multipart/related;
      boundary="_017_AMSPR04MB42366AB74EC83FB06957901993F0AMSPR04MB423eurprd_";
      type="multipart/alternative"
MIME-Version: 1.0
X-MS-Exchange-Transport-CrossTenantHeadersStamped: AMSPR04MB422
Return-Path: me@mydomain.co.uk
X-EOPAttributedMessage: 0
Received-SPF: Pass (protection.outlook.com: domain of mydomain.co.uk
 designates 157.56.112.144 as permitted sender)
 receiver=protection.outlook.com; client-ip=157.56.112.144;
 helo=emea01-am1-obe.outbound.protection.outlook.com;
Authentication-Results: spf=pass (sender IP is 157.56.112.144)
 smtp.mailfrom=me@mydomain.co.uk;
X-Forefront-Antispam-Report: CIP:157.56.112.144;CTRY:US;IPV:NLI;IPV:NLI;EFV:NLI;
X-MS-Exchange-Transport-CrossTenantHeadersStripped: AM1FFO11FD030.protection.gbl
X-MS-Exchange-Transport-CrossTenantHeadersPromoted: AM1FFO11FD030.protection.gbl
X-Microsoft-Antispam: BCL:0;PCL:0;RULEID:;SRVR:DBXPR03MB144;