Is it possible to transmit a Business Consent (authorization) request for an unincorporated business, a partnership or a trust using T2 EFILE software? 

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Yes, authorization requests transmitted using T2 EFILE software are valid for all business types, not just incorporated businesses.

Therefore, if you need an authorization for a business number (BN) associated with a sole proprietor, a partnership or a trust to access, for example, payroll or GST/HST accounts, you can use T2 software to transmit the authorization request via EFILE. You will need a valid EFILE number and a password for the transmission.

Note that the CRA does not post information related to a T3 trust return online yet. If you are an authorized representative for a BN issued to a trust, you will only be able to access the information associated with that BN (e.g., payroll or GST/HST information). 

When completing the authorization form in the T2 software, you must always indicate the BN of the payroll program or HST/GST account, not a SIN or a trust number. The name associated with the BN (e.g., the sole proprietor or the trustee of a trust) should be entered as the authorized signing officer. The signature page must be signed prior to transmitting the authorization request.

Note that the BN as well as the business activity code (NAICS) should be entered on the ID form to allow the transmission of the authorization. The NAICS code will not be transmitted to the CRA with the authorization; thus, any activity code can be selected.

https://www.canada.ca/en/revenue-agency/services/e-services/e-services-businesses/business-account.html