Send a copy of PMPro Approval admin notification emails to users that have the pmpro_approvals capability. This should include users that has the pmpro_approver role or the pmpro_membership_manager role role.

pmpro-approvals-bcc-admin-emails-to-users-with-pmpro-approvals-capability.php

<?php
/**
 * Bcc admin approval emails to users with pmpro_approvals capability.
 *
 * 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 pmpro_approvals_bcc_admin_notification_emails( $headers, $email ) {
	$approval_admin_email_templates = array(
		'admin_approved',
		'admin_denied',
		'admin_notification_approval',
	);

	// Is this email an approvals admin notification email?
	if ( ! in_array( $email->template, $approval_admin_email_templates ) ) {
		return $headers;
	}

	// Get all users with pmpro_approvals capability.
	$users_with_capability_pmpro_approvals = get_users(
		array(
			'capability' => 'pmpro_approvals',
			'fields'     => 'user_email',
		)
	);

	// Remove site admin email from array.
	$users_with_capability_pmpro_approvals = array_diff( $users_with_capability_pmpro_approvals, array( get_bloginfo( 'admin_email' ) ) );

	// Add Bcc to headers.
	if ( ! empty( $users_with_capability_pmpro_approvals ) ) {
		$headers[] = 'Bcc:' . implode( ',', $users_with_capability_pmpro_approvals );
	}

	return $headers;
}
add_filter( 'pmpro_email_headers', 'pmpro_approvals_bcc_admin_notification_emails', 20, 2 );