Exchange 2010 not allowing delivery from sender

"Mailbox unavailable" implies the e-mail address of the recipient doesn't exist.  

Have the sender quadruple-check the address he's sending to, and maybe have him send the e-mail to more than one recipient address so you'll see if it gets through at all and be able to see the e-mail address that fails.

Please make sure mailbox exists.

How did you configure mailbox is it POP or IMAP?

mailbox is ok, users has been using it for 5 years and it's not full

We both mean "make sure the recipient e-mail address is correct", because the error message strongly implies the sender is using the wrong e-mail address.

the address is connect anything we send to caepiping.com bounces back
they are not on a black list, I get the following bounce

Diagnostic information for administrators:
Generating server: server-3.bemta.az-b.us-east-1.aws.symcld.net
info@caepiping.com
#< #5.0.0 smtp; 550-Requested action not taken: mailbox unavailable> #SMTP#
Original message headers:
Return-Path: <joe@xxx.com>
Received: from [67.xxx.xxx.xxx] (using TLSv1.2 with cipher DHE-RSA-AES256-GCM-SHA384 (256 bits))
      by server-3.bemta.az-b.us-east-1.aws.symcld.net id D2/B1-07445-D38E12E5; Fri, 17 Jan 2020 17:00:45 +0000
X-Brightmail-Tracker: H4sIAAAAAAAAA+NgFrrGKsWRWlGSWpSXmKPExsXiYFPlpGv7QjH
  O4PoMPYulve+ZHBg9bp5fwhLAGMWamZeUX5HAmvF39gv2gk07GCtOtGxjaWBcsomxi5GLQ0jg
  IKPEx78LWboYOTnYBPQk/s76AJTg4BAR0JVoPWgOEhYWEJX4tfQRK4gtIiAlcf/NMyhbT+Lst
  /eMIDaLgKrE5mlfmUBsXgF/iZcbJ4GNZBQQk/h+ag1YnFlAXOLWk/lgtoSAiMTDi6fZIGxRiZ
  eP/7FC2IoSxzt6GCFsU4mdE26wQPR2MkrMOC0MMV9Q4uTMJywTGAVmIRk7C0nZLCRlEPE8iWO
  LlzBD2DoSC3Z/YoOwtSWWLXzNDGOfOfCYCVNcTeLw/BnsELaUxO8XW1lnAYOOWWAuo8TTzl1Q
  C/QkXqzshrIVJaZ0P2RfwMi7itE0qSgzPaMkNzEzR9fQwEDX0NBI11DXxFQvsUo3Sa+0WDc1s
  bhE11AvsbxYr7gyNzknRS8vtWQTIzBaUwoYdXcwtn56q3eIUZKDSUmU12SjYpwQX1J+SmVGYn
  FGfFFpTmrxIUYZDg4lCV7m50A5waLU9NSKtMwcYOKASUtw8CiJ8K5+BpTmLS5IzC3OTIdInWK
  05Jjwcu4iZo6Pq5YAye8gUoglLz8vVUqctxGkQQCkIaM0D24cLLldYpSVEuZlZGBgEOIpSC3K
  zSxBlX/FKM7BqCTMmw5yFU9mXgnc1ldABzEBHTTBWQ7koJJEhJRUA5O60z3laPbO1SdKX9vvm
  MSlYyuo5rF45tI+lwmTUtM4Mt64Cd56lxDy9f0h3x1aczU83pz819Rx9f6rm7PMzHzCt16ZZD
  TzWemUn8uCOesdry2PuJTTL+/h9eUS2zOtisR5dl/nPU+vYzoRfWP/Y6nYp4c+sUZd7mvQ3Oj
  /5eSnXRefR4UVHG18wsPdX639501O6ccnaXKnNNTrJjnvvJpWmKXxSUJXOsfh5iT2mXMtOB/N
  6a4+YmT6Z6FY+Q6FWOtzTJMXfnbclbkmxqdCNOJih76tpHe0yrwPFx4bP/AxmLOFJz2liZ/jz
  7cERjF3eRG/1uk9+Rs/aC9lOuahm+Eqm7CoOfDhiaC1yb5+bkosxRmJhlrMRcWJADrzC9jpAw
  AA
X-Env-Sender: joe@xxx.com
X-Msg-Ref: server-21.tower-391.messagelabs.com!1579280444!1245207!1
X-Originating-IP: [64.xxx.xxx.xxx]
X-SYMC-ESS-Client-Auth: outbound-route-from=pass
X-StarScan-Version: 9.44.25; banners=-,-,-
Received: (qmail 28213 invoked from network); 17 Jan 2020 17:00:45 -0000
Received: from xxx.com (HELO server.DOMAIN.xxx.PVT) (64.60.122.66)
  by server-21.tower-391.messagelabs.com with ECDHE-RSA-AES256-SHA encrypted SMTP; 17 Jan 2020 17:00:45 -0000
Received: from server.DOMAIN.xxx.PVT ([fe80::31cd:af1a:7ab2:a434]) by
 server.DOMAIN.xxx.PVT ([fe80::31cd:af1a:7ab2:a434%10]) with mapi id
 14.03.0123.003; Fri, 17 Jan 2020 09:00:43 -0800
From: "Joe " <joe@xxx.com>
To: "info@caepiping.com" <info@caepiping.com>
Subject: Sam
Thread-Topic: Sam
Thread-Index: AdXNV14fsLvd6+M3RsC2M6HkyBu/BA==
Date: Fri, 17 Jan 2020 17:00:43 +0000
Message-ID: <02EDE436A1946445A80AB99F693064512D56439D@BAILEY.DOMAIN.KSNINC.PVT>
Accept-Language: en-US
Content-Language: en-US
X-MS-Has-Attach: yes
X-MS-TNEF-Correlator:
x-originating-ip: [192.168.1.119]
x-pp-proceessed: b9bacbf4-164f-4088-a81f-856d41e5bc7a
Content-Type: text/plain
MIME-Version: 1.0

If anything you send to that domain bounces back, then they have a problem on their end. Could be they've installed new security software like a firewall and didn't configure correctly.

we tried sending an email from a gmail account and that worked ok

Right, as did my Yahoo account.  It looks as if they're blocking mail from your domain for some reason.  You should reach out to their technical people to see if they can look at the problem from their side.

Joe,

Go to mxtoolbox.com and look up your own domain. If it returns errors like "no dmarc found" it's a problem where caepiping's security doesn't like your domain. So it could be a config issue on your end combined with a security issue on their end.

the address is connect anything we send to caepiping.com bounces back
they are not on a black list, I get the following bounce

It's not them that is on a black list, it might be you guys. Although it is slightly strange that you would have a problem with only one domain in that case, but maybe they are using some odd black list.

Anyway, check your domain/IP on mxtoolbox as suggested, and in the meantime ask the recipient to whitelist your domain.

#< #5.0.0 smtp; 550-Requested action not taken: mailbox unavailable> #SMTP#"

Could be two things,

1- User mailbox has not being created, you need to add the mailbox.
2- The user does not have the right SMTP for Inbound/Outbound and thus you get this error.