This recipe will add some shortcodes to emails.

my-pmpro-custom-email-data-shortcodes.php

<?php
/**
 * This recipe will add some shortcodes to emails.
 *
 * by default the $data array that controls the email shortcodes is loaded
 * conditionally, depending on the type of email being sent. This will
 * add certain fields to emails if they are not available for that email template.
 *
 * You can add this recipe to your site by creating a custom plugin
 * or using the Code Snippets plugin available for free in the WordPress repository.
 * Read this companion article for step-by-step directions on either method.
 * https://www.paidmembershipspro.com/create-a-plugin-for-pmpro-customizations/
 */
function my_pmpro_custom_email_data_shortcodes( $data, $email ) {
	$user = get_user_by( 'email', $data['user_email'] );

	global $wpdb;

	$invoice = new MemberOrder();

	$sql = "SELECT id FROM $wpdb->pmpro_membership_orders WHERE user_id = $user->ID ORDER BY timestamp DESC LIMIT 1";

	$id = $wpdb->get_var( $sql );
	$invoice->getMemberOrderByID( $id );

	if ( ! isset( $data['invoice_total'] ) && empty( $data['invoice_total'] ) ) {
		$data['invoice_total'] = pmpro_formatPrice( $invoice->total );
	}
	if ( ! isset( $data['invoice_id'] ) && empty( $data['invoice_id'] ) ) {
		$data['invoice_id'] = $invoice->code;
	}
	if ( ! isset( $data['invoice_date'] ) && empty( $data['invoice_date'] ) ) {
		$data['invoice_date'] = date_i18n( get_option( 'date_format' ), $invoice->timestamp );
	}
	if ( ! isset( $data['billing_address'] ) && empty( $data['billing_address'] ) ) {
		$data['billing_address'] = pmpro_formatAddress(
			$invoice->billing->name,
			$invoice->billing->street,
			'', //address 2
			$invoice->billing->city,
			$invoice->billing->state,
			$invoice->billing->zip,
			$invoice->billing->country,
			$invoice->billing->phone
		);
	}

	return $data;
}
add_filter( 'pmpro_email_data', 'my_pmpro_custom_email_data_shortcodes', 10, 2 );