$('#year-submit').value = $('#year').value;

<form method="get">
    <select id="year" name="...">
        <option value="" selected="selected" hidden>Select Year...</option>
        <option>2018</option>
        <option>2019</option>
    </select>
</form>
<form method="get">
    <input type="hidden" id="year-submit" name="..." />
    ...
</form>