How to insert data into meta box from another plugin?

The meta boxes are irrelevant. Meta boxes are just a UI for adding arbitrary forms and data to the classic editor.

What matters is how and where the data is stored. Thankfully the code you included reveals this. From your code we can see that the saved values are stored as post meta:

$faqpress_ticket_username = get_post_meta( $post->ID, 'faqpress_ticket_username', true );
$faqpress_ticket_email    = get_post_meta( $post->ID, 'faqpress_ticket_email', true );

So if you want to store the data in the same place as the meta boxes then you need to store it as post meta also. Storing post meta is as simple as using a corresponding update_post_meta():

update_post_meta( $post_id, 'faqpress_ticket_username', $value );
update_post_meta( $post_id, 'faqpress_ticket_email', $value );

You just need to make sure the $post_id and $value variables are populated appropriately.