Thank you for pointing me in right direction. I now started looking in ssl_error_log and noticed this line:
PHP Parse error: syntax error, unexpected '*', expecting function (T_FUNCTION) or const (T_CONST) in /var/www/html/eng-mod/lib/pkp/lib/vendor/phpmailer/phpmailer/class.phpmailer.php on line 163
I have probably by mistake entered * while searching why emails are not being sent. This has solved problem with window closing after clicking send.
Finally, error message has appeared 
SMTP connect() failed. https://github.com/PHPMailer/PHPMailer/wiki/Troubleshooting, referer: https://web-site/index.php/ijem/management/settings/access
I have gone through the troubleshooting and I cannot find anything relating to this problem, especially when I have one service which is using SMTP and it is working normally. So it came to me that I have recently tested the sendmail from the command line and it works just fine. I have turned SMTP to OFF in config.inc.php and OJS started to send emails.
The problem with SMTP still persists, but at least I have solve the problem.
Thank you for the support.