Is it permissible to return to work for a company that was using unlicensed software, while it is trying to complete the licensing, knowing that the company's capabilities allow it to purchase all licenses, and the system might be a one-year contract?

Working in the company is permissible in what is permissible. The questioner has done well by advising and correcting the situation through purchasing licenses. There is no harm in returning to the previous job, provided that pirated software is avoided and advice is given to complete the licensing. Striving for what is lawful brings Allah's facilitation and provision, in accordance with His saying, the Most High: "And whoever fears Allah - He will make for him a way out And will provide for him from where he does not expect. And whoever relies upon Allah - then He is sufficient for him. Indeed, Allah will accomplish His purpose. Allah has already set for everything a [decreed] extent."