Replace "sendmail" with (a link to) the script, and forward all system mails via free Mailgun acct to your chosen external address

sendmail-free-mailgun.sh

#!/bin/bash

# Documentation can be found on either of following blogs (with mirrored content):
# https://pindertek.net/2018/07/04/sendmail-free-mailgun/
# https://craigphicks.github.io/2018/07/04/sendmail-free-mailgun/

# NOTE: root permission required to write to /var/log.
# Choose another log location if that will not be suitable.
Logfile=/var/log/sendmail-dummy.log
if [[ $EUID -ne 0 ]]; then
    Logfile=${HOME}/sendmail-dummy.log
fi    
Tmpf=$(mktemp -t sendmail-dummy-ml-XXXXXX.txt)
TmpCurlLog=$(mktemp -t sendmail-dummy-re-XXXXXX.txt)
trap 'rm -f ${Tmpf} ${TmpCurlLog}' 0

Date=$(date +%F-%T)
echo "[$Date] Caller: $(caller)" >>${Tmpf}
echo "[$Date] Caller: $0" >>${Tmpf}
echo "[$Date] Args: ${@}" >>${Tmpf}
echo "[$Date] Content:" >>${Tmpf}
while read line ; do
    echo $line  >>${Tmpf}
done
echo "" >>${Tmpf}


# If you have signed up free mailgun account then login and go to url:
#   https://documentation.mailgun.com/en/latest/quickstart-sending.html#send-via-api
# to see the approriate values for the following variables  
MailgunDomain="()"
Key="()"
FromAddr="()"
ToAddr="()"

curl -s --user "api:${Key}" "https://api.mailgun.net/v3/${Key}/messages" \
     -F https://api.mailgun.net/v3/${MailgunDomain}/messages \
     -F from=" <$FromAddr>" \
     -F to="${ToAddr}" \
     -F subject='Notification' \
     -F text="<${Tmpf}" > ${TmpCurlLog}
rc=$?

echo "----------------------------------------" >> ${Logfile}
cat ${Tmpf} >> ${Logfile}
echo "----------------------------------------" >> ${Logfile}
echo "[$Date] curl result = $rc" >> ${Logfile}
cat ${TmpCurlLog} >> ${Logfile}
echo "" >> ${Logfile}
echo "++++++++++++++++++++++++++++++++++++++++" >> ${Logfile}