Is there any way to send SMS to another device using internet?
The only way to accomplish this is to use an online SMS gateway, which means you send the message to the service provider via the internet, and they forward it to the recipient over SMS. There are several service providers for this, but mostly they require a subscription, i.e. they're not free. Just google for "sms gateway" to find them.

Some service providers have Android app support, but this depends on your region and the selected service provider.

Note that most service providers don't allow you to use your own number as the sender, therefore the recipient may have a hard time replying to you.