Is it permissible for me to join as a partner in a new industrial company that belongs to a group I work for, knowing that its activity aligns with the activity of another company within the group, that my experience is personal, and that the work will be outside official working hours?

The questioner incurs no sin by entering as a partner in the aforementioned industrial company, whether its activity aligns with the company he is currently associated with or not, and whether he gained his experience from the company he works for or not. The important thing is that his work in the new company is outside his official working hours, because his benefits during these hours belong to the company he works for.