cd
pecl download mailparse
tar -xvf mailparse-3.0.2.tgz
cd mailparse-3.0.2/
phpize
./configure
sed -i 's/#if\s!HAVE_MBSTRING/#ifndef MBFL_MBFILTER_H/' ./mailparse.c
make
sudo mv modules/mailparse.so /usr/lib/php/201603
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Since PHP-5.6 is EOL (end of life... deprecated... dead... hackable...) you may find you have to use some older version (not latest) to match PHP-5.6 which likely sets your starting point.
If I did the instructions above + had problems, I'd contact the mailparse developer(s) asking about which mailparse version I should use with PHP-5.6 as they'll likely know if there's downlevel version you must use.