Send newsletter subscription emails to external database

Hello,

Been working on website for a while, and got left with 1 problem :). I need to create or use newsletter subscription pop-up window, but for all emails that are being used to subscribe to newsletter i need to send to external Newsletter provider like MailChimp, Campaign Moniter and other serverice database that i created.

The provider gave me short newsletter window HTML/CSS/JavaScript code, but that one is way too simple :
backticks
<div class=”sbscr_cont”>
<input id=”sbscr_d” type=”hidden” value=”https://subscribe.reklamainternetu.lt/submit.php?h=214baaa0cc15928fb475480d0017d064&#8243; />
<input id=”sbscr_l” type=”hidden” value=”LT” />
<h2 class=”sbscr_heading”>You subscribed to our newsletter</h2>
<p>E-Mail: <input id=”sbscr_e” type=”text” /></p>
<div id=”sbscr_er_eml” class=”sbscr_msg_err” style=”display: none”>
Please enter correct e-mail
</div>
<div id=”sbscr_er_agr” class=”sbscr_msg_err” style=”display: none”>
We can’t register you.
</div>
<div id=”sbscr_er_srv” class=”sbscr_msg_err” style=”display: none”>
You can’t subscribe, because of technical problems
</div>
<div id=”sbscr_ms_ok” class=”sbscr_msg_ok” style=”display: none”>
Thank you for subscribing.
</div>
<p><input id=”sbscr_a” type=”checkbox” checked=”checked” /><label for=”sbscr_a”>I confirm to get newsletter to email</label></p>
<p><input id=”sbscr_b” type=”button” value=”Prenumeruoti” /></p>
</div>
<script type=”text/javascript” src=”https://subscribe-js.reklamainternetu.lt/js/jquery-1.5.min.js?214baaa0cc15928fb475480d0017d064″></script&gt;
<script type=”text/javascript” src=”https://subscribe-js.reklamainternetu.lt/js/sbscr-min.js?214baaa0cc15928fb475480d0017d064″></script&gt;
<noscript>
<div class=”sbscr_cont”>
U?siprenumeruokite mūs? naujienlai?k?
</div>
</noscript>
backticks

I need some kind of newsletter, that when person presses “Subscribe”, email will be send to this link -> https://subscribe.reklamainternetu.lt/submit.php?h=214baaa0cc15928fb475480d0017d064&#8243;

Any solutions?

Thank you.