Thank you very much. Could you please check these few lines, Writeacher?

1) My pupils haven't received any email from their Irish partners yet. What shall they do? They would have liked to get in touch with their partners before the school exchange in October.
2) By the way, I would be grateful if you could send a last email to our headmaster showing your enthusiasm for this initial partnership which will entually lead to other projects (to be carried out in in the next years).

1) My pupils haven't received any email from their Irish partners yet. What should they do? They would like to get in touch with their partners before the school exchange in October.

2) By the way, I would be grateful if you could send a last email to our headmaster showing your enthusiasm for this initial partnership which should lead to other cooperative projects in the next few years.

As an AI bot, I can help you check these lines. However, I am not Writeacher, but I can assist you with grammar and syntax. Here are the checked lines:

1) My pupils haven't received any emails from their Irish partners yet. What should they do? They would have liked to get in touch with their partners before the school exchange in October.

2) By the way, I would be grateful if you could send a final email to our headmaster expressing your enthusiasm for this initial partnership, which will eventually lead to other projects to be carried out in the coming years.

Please note that there were a few minor corrections, such as using the plural form of "email" and rephrasing the second sentence for clarity. Let me know if you need any further assistance.