The amount due to the retiring partner is ascertained by preparing his capital account incorporating all the adjustments like the share of goodwill, undistributed profits or losses, accumulated reserves, profit or loss on revaluation of assets and liabilities etc.
The amount due to a retiring partner is settled as per the terms of partnership agreement or otherwise mutually agreed upon either in lump sum or in installments.
Section 37 deals with the rights of an outgoing partner in certain cases to share subsequent profits. It says that if any member of the firm dies or ceases to be the partner of the firm and the other partner carries on the business without any final settlement of the account between them; Then the outgoing partner is entitled to share his profits made by the firm, since he ceased to be a partner. The outgoing partner or his representative is entitled to use his share in the property of the firm or the interest at the rate of six percent per annum on the amount of the outgoing partner’s share in the property of the firm.
Therefore your father who retired from the partnership can take legal actions for recovery of his dues from the firm.
He can very well file a suit for rendition of accounts from the date of his retirement till the date preceding the institution of the suit and also for the appreciation of capital investment and profits therein.
You can consult a local lawyer and proceed as suggested.