[Plugin: Post From Site] Checkbox instead of select multiple category: how to?

Hi, Is it possible to have a list of checkboxes instead of a multiple select for category selection in the front end writer? I managed to have the list of checkboxes in the front-end by changing these lines

public function get_taxonomy_list( $taxonomy ){
		$terms = get_terms($taxonomy, array(
			'hide_empty' => 0
		));
		if (!$terms || empty($terms)) return '';
		//preg_match_all('/\s*<option class="(\S*)" value="(\S*)">(.*)<\/option>\s*/', $terms, $matches, PREG_SET_ORDER);
		$out = apply_filters( 'pfs_taxonomy_label', "<label for='terms_$taxonomy'>Seleziona i corsi</label>", $taxonomy );
		$out .= "<select id='terms_$taxonomy' name='terms_$taxonomy' size='4' multiple='multiple'>";
		foreach ($terms as $term){
			if (is_taxonomy_hierarchical($taxonomy))
				$out .= "<option value='{$term->term_taxonomy_id}'>{$term->name}</option>";
			else
				$out .= "<option value='{$term->name}'>{$term->name}</option>";
		}
		$out .= "</select><br />\n";
		return apply_filters("pfs_{$taxonomy}_list",$out);
	}

with these

public function get_taxonomy_list( $taxonomy ){
		$terms = get_terms($taxonomy, array(
			'hide_empty' => 0
		));
		if (!$terms || empty($terms)) return '';
		//preg_match_all('/\s*<option class="(\S*)" value="(\S*)">(.*)<\/option>\s*/', $terms, $matches, PREG_SET_ORDER);
		$out = apply_filters( 'pfs_taxonomy_label', "<label for='terms_$taxonomy'>Seleziona i corsi</label>", $taxonomy );
		foreach ($terms as $term){
			if (is_taxonomy_hierarchical($taxonomy))
				$out .= "<input class='{$term->term_taxonomy_id}' type='checkbox' value='{$term->term_taxonomy_id}' /> {$term->name}<br />";

			else
				$out .= "<input class='{$term->term_taxonomy_id}' type='checkbox' value='{$term->name}' /> {$term->name}";
		}
		$out .= "<br />\n";
		return apply_filters("pfs_{$taxonomy}_list",$out);
	}

but I guess I have to edit something else too, because now the post is posted without categories, even if I select them.
Any help would be appreciated!

https://www.ads-software.com/extend/plugins/post-from-site/