Yes. A spouse admitted in L-2 status is employment-authorized incident to that status and does not need a separate permit before starting work. Unmarried children under twenty-one may attend school in L-2 status but may not work.
The L-2 spouse rule is the most generous among these transfer categories
Employment authorization for a qualifying L-2 spouse arises from the status itself, which is why the annotated Form I-94 is generally what an employer asks to see during onboarding. The spouse may take a job with any employer, work for himself or study. Children in L-2 status may enrol in school and may not work.
Three practical points follow. The whole household's status depends on Bertrand's; if his L-1A ends because the U.S. business is sold or he leaves the group, the dependants' status ends with it and any job the spouse holds must stop.
The marriage must be legally valid, since a common-law partner does not qualify for L-2. And a child approaching twenty-one needs an independent plan well before the birthday, because derivative eligibility ends there rather than tapering.