Should be pretty simple. Just give your form an id
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<form id="the-form" method="POST" action="{{ route('sms.store') }}">
Give the submit button an id
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<button id="the-submit" type="submit" class="btn btn-primary">Save changes</button>
Then use jquery (since you're using bootstrap) to submit the form when the submit button is clicked.
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$(function() {
$('#the-submit').on('click', function(e) {
$('#the-form').submit();
});
});