Is the lender entitled to consider the debt and the capital he paid into the business as his share in the partnership after his partner violated the agreement?

The partnership is valid, and each partner owns a share of its capital proportional to what they paid, even if the capital contributions of the two partners differ. The friend's promise to repay the debt is not a condition for the partnership. You are permitted to collect your debt from his profits or capital without his permission if he is a defaulter, and this falls under the ruling of "al-Zafar" (obtaining one's right).