Web-based SMS gateways typically let you specify the message
originator, but as an alphanumeric field only.

The SMS originator address field contains a maximum of 12
octets.  One octet is used for specifying length, and another
for type-of-number.  Assuming type-of-number is D0 hex
(alphanumeric) as above, that leaves room for a maximum of 11
alphanumeric characters (((12 - 2) * 8) / 7) from the GSM
default alphabet.  And for most national numbering schemes, 11
characters isn't enough to represent a mobile/cellular number
in the usual international format.

The web site doesn't inspire much confidence when it makes silly
claims like:

"Global Coverage to over 175 countries. ... When you press 'SEND
MESSAGE' here, you can be sure that your recipient will receive
the SMS message within 20 seconds. There is no waiting around
here for foreign gateways to respond to the request."

John