Send SMS to the subscriber is possible through the operator’s SMS center. Directly access to the operator’s SMS center is handled either by the operator itself or by the intermediary office. The SMS center, as a rule, communicates with the "outside world", i.e. clients through the SMPP protocol. Communication to the SMS center is usually established via a VPN tunnel. In the case of the SMPP, the client (i.e., you) concludes an agreement with the operator (intermediary), establishes a VPN connection, then writes his code that "can" send PDU packets (which contain SMS) - read the SMPP protocol specification - it is freely available on the Internet) protocol SMPP SMS center and receive and process them.
As a rule, because of the specificity of the SMPP protocol, as well as because of the small difficulty in implementing the program for a programmer who did not have experience with the protocol, and because of the inexpediency of writing and his own individual SMPP application for small projects, the HTTP interface is used provided by an operator or an intermediary: in this case, you call a normal URL (it is called either "via" VPN, or the URL is public. In the values of the URL parameters (the SOAP variant is also possible) the authorization data, ie the login password) is specified, the parameters from which processed by the server, which is then consolidated through the channel transmits the data via SMPP SMS center. This scheme is designed to save the client from developing applications that use SMPP directly. The URL can look like this:
http://operator-vpn-server.ru:8080/http2smpp/send.app?login=xxx&pass=yyy&from=MYFIRM&to=7920XXXXXXX&txt=Hello%20World&my_msg_id=3F000022&resp=true
The principle of operation in this case comes down to the fact that the operator creates his own universal SMPP client-hub, which is connected to the SMS center of the operator at the output, and on the other hand accepts HTTP requests from outside from numerous clients, i.e. performs the role of HTTP traffic transcoder in SMPP protocol. Thus, the effect of simplified logic is achieved - there are many clients, and there is only one handler, thereby saving each consumer-client from developing their own SMPP applications. Moreover, it relieves the staff of tedious consultations in response to the claims of each client on the topic "I did everything right, but your SMPP does not work" :)
For the delivery of messages from the subscriber to the client (and the delivery status of the messages you send) is used again or SMPP, or you provide your URL, which will be called by the operator (intermediary) side to transfer data of your application.
In your case (say, the URL scheme is chosen) - and the data from the form that the visitor filled out is processed in some script, - you simply add the same URL specified above to the parameters (text) which you enter the necessary information: even though the text itself from the form, even just "Attention, the new form is filled!" - You decide.