The District Court for each county in Texas typically handles all family law (like probate and guardianship and adoptions). See if you can get online to the El Paso County site and look around and find some FAQs to direct you to the right phone number. If that doesn't work, just call any District Court number and tell them you are interested in obtaining a copy of or looking at the original (depending on where you are) of an OPEN adoption and ask who you need to talk to and the process, etc. Keep stressing it is an OPEN adoption. The only time I have ever seen a situation like this where it was actually not an open adoption was when the child was adopted out of state and the state of Texas was not involved in the complete process and therefore wasn't alerted to covering up the original birth cert.

Here's the link to Christopher's birth details (it's not the full cert but it lists his real parents):
https://familysearch.org/ark:/61903/1:1:VDF3-GRH

Since you're a relative (and I assume have the same surname..or someone close to you does). it would be easy enough to order a copy of the full birth cert. The El Paso County Clerk does this and the info on the procedure is detailed online at their site. You only need an "informational" copy for genealogical purposes...not certified. They'll make you show proof of relationship with copies of this and that.

That should get you going. You'll probably hit some road blocks because most adoptions are closed in that period and the clerks will try to give you grief, but just don't take no for an answer. You might want to try googling something like "Texas adoption law" to get familiar with the terminology and how things work.

Best of luck. Never give up.