Is it permissible to divide profits equally between two partners if one of them paid the full amount to the other so that he could enter with him as a partner with the same amount in an existing project?

There is no harm in establishing this company. The profit should be divided between the two partners according to an agreed-upon, known percentage, such as half or a third. This falls under Shirkat al-Inan if he contributes his capital and you contribute your capital, or Shirkat al-Mudharabah if he contributes his capital and you contribute your capital and effort. There is no objection to one partner's share of the profit being greater, provided the conditions of the partnership are met and the work is permissible.