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 I had a similar problem on Prestashop 1.7.6.4. , with the error "Connection timed out" with particular SMTP settings. Clients such as thunderbird and claws work without problems. Tcpdump shows timeout trying to manage the TLS handshake. 

Finally decided to use PHP-mail function instead of Swiftmailer:

1. Install Postfix and configure it in relay mode  https://www.linode.com/docs/guides/postfix-smtp-debian7 
2. Edit the php-config "sendmail_path = /usr/sbin/sendmail -t -i"

Some advantages are : 

• Postfix is easier to test, using the command line and enabling options of debugging.
• Postfix has a lot of configurable options to accomplish with your SMTP server requirements postfix config 

I just want to share another approach to solve it  (less patiently), if you have a self-manage the server.  

 I had a similar problem on Prestashop 1.7.6.4. , with the error "Connection timed out" with particular SMTP settings. Clients such as thunderbird and claws work without problems. Tcpdump shows timeout trying to manage the TLS handshake. 

Finally decided to use PHP-mail function instead of Swiftmailer:

1. Install Postfix and configure it in relay mode  https://www.linode.com/docs/guides/postfix-smtp-debian7 
2. Edit the php-config "sendmail_path = /usr/sbin/sendmail -t -i"

Some advantages are : 

• Postfix is easier to test, using the command line and enabling options of debugging.
• Firstly you can be sure that your SMTP settings are correct and work. 

I just want to share another approach to solve it  (less patiently), if you have a self-manage the server.  

 I had a similar problem on Prestashop 1.7.6.4. , with the error "Connection timed out" with particular SMTP settings. Clients such as thunderbird and claws work without problems. Tcpdump shows timeout trying to manage the TLS handshake. 

Finally decided to use PHP-mail function instead of Swiftmailer:

1. Install Postfix and configure it in relay mode  https://www.linode.com/docs/guides/postfix-smtp-debian7 
2. Edit the php-config "sendmail_path = /usr/sbin/sendmail -t -i"

Some advantages are : 

• Postfix is easier to test, using the command line and enabling options of debugging. Firstly you can be sure that your SMTP settings are correct and work on this side. 
• Postfix implements pool. 

I just want to share another approach to solve it  (less patiently), if you have a self-manage the server.  

 I had a similar problem on Prestashop 1.7.6.4. , with the error "Connection timed out" with particular SMTP settings. Clients such as thunderbird and claws work without problems. Tcpdump shows timeout trying to manage the TLS handshake. 

Finally decided to use PHP-mail function instead of Swiftmailer:

1. Install Postfix and configure it in relay mode  https://www.linode.com/docs/guides/postfix-smtp-debian7 
2. Edit the php-config "sendmail_path = /usr/sbin/sendmail -t -i"

Some advantages are : 

• Postfix is easier to test, using the command line and enabling options of debugging. Firstly you can be sure that your SMTP settings are correct and work on this site. 
• Postfix implements pool. 

I just want to share another approach to solve it  (less patiently), if you have a self-manage the server.