You have to modify Mage_ImportExport_Adminhtml_ExportController::exportAction (of course don't change the file directly, but overwrite the controller update safe).
Change this part:
return $this->_prepareDownloadResponse(
$model->getFileName(),
$model->export(),
$model->getContentType()
);
to:
$filename = $model->getFileName();
$content = $model->export();
file_put_contents(Mage::getBaseDir('var') . DS . 'importexport' . DS . $filename, $content);
return $this->_prepareDownloadResponse(
$filename,
$content,
$model->getContentType()
);
This should save the file in the given directory. Of course you can modify the filename $filename
at that point.