554 error to 1 & 1 hosted domain

[#1]

There was an old thread on this topic, apparently now locked.

Mail sent by me to a friend with email address on a domain hosted by 1 & 1 is generating responses like

Final-recipient: rfc822; xxxx@xxxxxxx.org.uk
Diagnostic-Code: smtp; 554-kundenserver.de (mxeue112) Nemesis ESMTP Service not available

The mail is apparently delivered, though.  A message from her to me received a similar response and was not delivered, although we originally assumed this was because it contained just a single URL which I wanted.

I can provide the full error message if required but I will need to spend a little time redacting the meaningful addresses and names.

[#2]

Hi @Shentar,

Is your email service provided by ourselves, or a third party (for example a domain hosted elsewhere/Gmail/Hotmail etc,)? 

I'd also suggest it would be useful to provide a header if this was at all possible.