Need short form integration with 3rd party

I would really appreciate some assistance. I currently use gravity forms on my real estate website as a call to action contact form. Here is an example:
http://www.wesellsarasota.com/idx/mls-m5835395-5853_e_fairwoods_cir_sarasota_fl_34243

I would love to be able to take the basic contact info from Gravity forms submissions and update my 3rd party real estate lead management software. Anyway, the third party company has their own contact form creator to create form html for me to embed on my website that will integrate with their database automatically. .....but I would much rather use gravity forms instead for many reasons.

I need assistance. I understand I need to use the gforms_after_submission hook, but unsure how to do it.

Here is the HTML form the 3rd party provided that would integrate with their database.

<form action="." method="POST" onsubmit="this.setAttribute('action', 'http://emails.dsagentreach.com/webservices/remoting.asmx/AddContact'); return true;">
	<input type="hidden" name="PublicID" value="I HAVE MY ID #WHICH GOES HERE" />
	<input type="hidden" name="LeadSourceGroup" value="WSS IDX Sidebar - Gravity Forms" />
	<input type="hidden" name="RedirectURL" value="http://www.MYWEBSITENAME.COM/redirect" />
	<table>
		<tbody>
		<tr><td><label class="dsar_1">First Name</label></td><td><input type='text' name='dsar_1' class='text textinput' /></td></tr>
		<tr><td><label class="dsar_2">Last Name</label></td><td><input type='text' name='dsar_2' class='text textinput' /></td></tr>
		<tr><td><label class="dsar_13">Home Phone</label></td><td><input type='text' name='dsar_13' class='text textinput' /></td></tr>
		<tr><td><label class="dsar_18">Email</label></td><td><input type='text' name='dsar_18' class='text textinput' /></td></tr>
		<tr><td><label class="dsar_1050">Referring URL</label></td><td><input type='text' name='dsar_1050' class='text textinput' /></td></tr>
		<tr><td><label class="dsar_5245">Referral</label></td><td><input type='text' name='dsar_5245' class='text textinput' /></td></tr>

		<tr>
			<td colspan="2">
				<input type="submit" name="submit" value="Submit" />
			</td>
		</tr>
		</tbody>
	</table>
</form>