The filters are already stored in the session, so you could write some PHP to grab those and then build your {fabrik view=list} plugin declaration from that.
The filters settings are stored using the following keys:
key = com_fabrik.list1_com_fabrik_1.filter.value
key = com_fabrik.list1_com_fabrik_1.filter.condition
key = com_fabrik.list1_com_fabrik_1.filter.join
key = com_fabrik.list1_com_fabrik_1.filter.no-filter-setup
key = com_fabrik.list1_com_fabrik_1.filter.hidden
key = com_fabrik.list1_com_fabrik_1.filter.key
key = com_fabrik.list1_com_fabrik_1.filter.search_type
key = com_fabrik.list1_com_fabrik_1.filter.match
key = com_fabrik.list1_com_fabrik_1.filter.full_words_only
key = com_fabrik.list1_com_fabrik_1.filter.eval
key = com_fabrik.list1_com_fabrik_1.filter.required
key = com_fabrik.list1_com_fabrik_1.filter.access
key = com_fabrik.list1_com_fabrik_1.filter.grouped_to_previous
key = com_fabrik.list1_com_fabrik_1.filter.label
key = com_fabrik.list1_com_fabrik_1.filter.elementid
key = com_fabrik.list1_com_fabrik_1.filter.raw
Most of which you wouldn't need to access, what I think you would need is the element id and the value.
PHP:
// Get the list Model for list id 1
$listModel = JModel::getInstance('List', 'FabrikFEModel');
$listModel->setId(1);
$app = JFactory::getApplication();
// When stored in the session this lists filters are stored in this namespace:
$context = 'com_fabrik.list' . $listModel->getRenderContext() . '.filter';
// Get the element filter keys (which will be in the format `tablename`.`elementname)` which have filters attached to them:
$elements = $app->getUserState($context . '.key');
// Get the values
$values= $app->getUserState($context . '.value');
// Debug out what the filters are:
for ($i = 0; i < count($elements); i++) {
echo $elements[$i] . ' filter value = ' . $values[$i];
}