Everything turned out after the recommendation of Turbo SMS TP.
What I did on the service side in the gateway settings:
1. Changed API login.
2. Changed the API password.
3. Left only SOAP.
In OneBox, I registered this new data in the settings.
Everything worked correctly.
http://prntscr.com/uxkeimIssue resolved.
Dima, thanks for the quick response!