We can use SP.MoveCopyUtil.moveFolder method to move the specified folder to the destination.
Example code:
<script type="text/javascript">
function moveFolder(){
ExecuteOrDelayUntilScriptLoaded(function(){
var context = SP.ClientContext.get_current();
SP.MoveCopyUtil.moveFolder(context,"https://mytestsite.sharepoint.com/Shared%20Documents/Folder1/Folder2/Active/02_NamedFolder","https://mytestsite.sharepoint.com/Shared%20Documents/Folder1/Folder2/Inactive/02_NamedFolder");
context.executeQueryAsync(function(){
alert("success.");
},function(sender, args){
alert('request failed ' + args.get_message() + '\n' + args.get_stackTrace());
});
}, "sp.js");
}
</script>
<input type='button' onclick="moveFolder()" value="Move Folder"/>
Reference: How to use SP.MoveCopyUtil to copy (or move) files (or folders)