How can I sign and send the EIN request form if I am outside the U.S.? Is there any service you can recommend, just to sign papers and submit, when required?

Remote Businesses
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As a foreign non-U.S. resident you can either call or fax your EIN application. More information is available on the IRS site and many company formation companies can complete this for a fee.

Recommendations of companies that specialize in this are Doola and Clemta.