He is employment-authorized incident to L-2 status, so U.S. work is permitted. Continuing to invoice Ontario clients from an American address raises tax and business-registration questions that immigration status does not answer.
Work permission and tax residence are different files
L-2 spouse employment authorization attaches to the status itself, so he may take a job or work for himself in the United States without a separate application, though many spouses still obtain the document because employers ask for something to photocopy. That settles immigration. It does not settle whether his consulting income becomes taxable in the United States once he lives there, whether his Ontario corporation now has an American presence, or whether his clients' contracts permit the work to be performed abroad. Those questions belong to an accountant who works across both systems and should be asked before the move rather than at the first filing deadline. Children under twenty-one in L-2 status may attend school; they may not work, and their status ends with the parent's.
Hypothetical example: the spouse plans to sell hand-drawn textile patterns to U.S. customers after arrival. The first review should confirm the admission classification shown on the electronic record and then obtain tax advice about the activity and any Canadian corporation. The status record settles work authorization; it does not settle registration, income reporting or sales-tax obligations. Sequence the business launch after both reviews, keep invoices and contracts in order, and do not rely on an employer's informal understanding of immigration rules as proof of the spouse's permission.