How to send messages from a site if PHP's mail() function was blocked?

Question

PHP

Recently, a client asked to fix some functions of the site on Wordpress, including sending messages to the mail from the feedback form, which did not reach the address.
In the end, it turned out that due to numerous viruses in the site directory (and there are 8 of them), the PHP mail() function was blocked. In response to a support email, I received the following response:

You need to not only remove all viruses, but also take steps to eliminate the vulnerabilities through which they penetrate the site.
Once all viruses have been removed and vulnerabilities fixed, write to us. Then we will check your sites, and if everything is in order, we will unblock all functions for normal work.

The problem is that I only have access to my directory, which I successfully cleaned. The rest of the sites are handled by another person who does not know when they will be dealt with.
The question is - is it possible to somehow bypass the hosting blocking for sending messages or are there third-party services that provide such a service?

Answer 1

Send emails through some service with REST API. For example Mandrill

Answer 2

leave PHPmailer and everything is ok

Answer 3

Yes, I’m trying to set up smtp, but so far it doesn’t work ...
it hangs when sending a test ...