A project invitation is a business communication, not a family member’s immigration document. An eligible L spouse can be employment-authorized incident to valid status with appropriate evidence; dependent children do not receive that spousal benefit.
Read the invitation for the activity it actually proposes
A message may invite the household to a reception, ask a spouse to help with administration, or list a relative among project personnel. Those are different activities. Identify who would perform services and where before assuming the welcome covers paid or unpaid work. L-2 eligibility concerns a qualifying spouse or unmarried child under 21. Review each traveller’s status record and dates; adding a name to the team directory cannot establish the relationship, valid status or authority to work.
The harder planning question is what the family does when the maximum is reached, because L-1B allows five years rather than the seven available in L-1A, and derivative status ends when the principal’s does. Since L-1B is capped at five years, the derivative timeline is bounded by whatever time the principal has left — which matters most when a child is approaching that birthday or a spouse is negotiating a multi-year role.