Need PHP expert to integrate HTML & PHP form into SMTP

Below I am including an HTML Form and the PHP code to send emails from a website.

I need an HTML, PHP, and a SMTP email expert that can make this form works with SMTP email settings.

Meaning I don't want to send emails from website via PHP Email.

I would like to send emails via SMTP email.

I hope this is clear, if not ask me questions.

IMPORTANT:

Automated bids will be eliminated.

And I want the code to be minimal and remain as similar as possible.

Budget is limited for this project.

*********** HTML MARKUP ***********
<form class="contact" action="consultations.php" method="POST">
<input name="name" placeholder="Name *" type="text" required="">
<input name="email" placeholder="Email *" type="email" required="">

<select id="findus" name="findus" required="">
<option value="" disabled="" selected="">How you find us? *</option>
<option value="Bing Search">Bing Search</option>
<option value="Yahoo Search">Yahoo Search</option>
</select>

<textarea name="message" required="" placeholder="How can we help you? *"></textarea>

<input name="captcha" type="text" required="" placeholder="* Type captcha here = LAW35">

<input value="Send email" type="submit">
</form>
*********** HTML MARKUP **********

*********** PHP CODE **********
<?php
function check_input($data)
{
$data = trim($data);
$data = stripslashes($data);
$data = htmlspecialchars($data);
return $data;
}

$name = check_input($_POST['name']);
$email = check_input($_POST['email']);
$findus = check_input($_POST['findus']);
$message = check_input($_POST['message']);
$captcha = $_POST["captcha"];

if(strtolower($captchaResult) == "law58") {

$formcontent="Name: $name \nEmail: $email \nHow you find us?: $findus \nMessage: $message";
$recipient = "emailATgmail.com";
$subject = "New Email";
$mailheader = "From: $email \r\n";

mail($recipient, $subject, $formcontent, $mailheader, '-fnoreplyATdomain.com') or die("Error!");
header('Location: https://domain.com/thanks/');
exit;
}

else {
header('Location: https://domain.com/wrong/');
exit;
}
?>
*********** PHP CODE **********