After a long troubleshooting we came out with the conclusion that this is not really a problem with the App but a combination of your server and the SMS library.
I logged in the server you provided and set up a new SMS dataset and, indeed, it was failing while sending the SMS with a message
Checking the Android logs it seems that the SMS library is crashing due to a problem with the UID of one DataEelement:
As you can see, that DataElement has a wrong ID, which also crashes in the DHIS App:
I think this can be solved by deleting that DataElement or modifying it directly in the DB (which I think is what caused the issue in the first place).
Anyway, I am going to report this issue on JIRA so the SMS library throws a better error and users can understand what is going on.
Hope this helps!
P.S -> Please note that I created some trash on your server, please discard those changes