Here is the current DNS setup:

 mx.example.com  3600    A   93.157.123.73
 example.com     3600    A   93.157.123.93
 www.example.com     3600    A   93.157.123.93
 mail.example.com    3600    A   93.157.123.72
 smtp.example.com    3600    CNAME   mail.example.com
 pop3.example.com    3600    CNAME   mail.example.com
 imap.example.com    3600    CNAME   mail.example.com
 panel.example.com   3600    CNAME   panel.example2.pl
 www.panel.example.com   3600    CNAME   panel.example2.pl
 ftp.example.com     3600    CNAME   example.com
 mysql.example.com   3600    CNAME   example.com
 pgsql.example.com   3600    CNAME   example.com
 *.example.com   3600    CNAME   example.com
 example.com     3600    MX  10 mx.example.com
 example.com     3600    NS  ns1.example2.pl
 example.com     3600    NS  ns2.example.pl
 example.com     3600    TXT     "v=spf1 redirect=_spf.example3.pl"

My client wants to have mail on his own server alfa.otherhost.com. Which entries do I have to update? Only the MX one?

 example.com     3600    MX  10 alfa.otherhost.com

or:

 example.com     3600    MX  10 mx.alfa.otherhost.com

Do I need to update POP, SMTP and IMAP entries too?