Citicorp, the country's second-largest banking organization, received final approval yesterday from the Federal Reserve for the acquisition of Fidelity Federal Savings and Loan of San Francisco.

This is the first takeover ever permitted of a troubled savings and loan by a bank holding company from another state. It also puts the New York giant in the backyard of the largest institution, BankAmerica Corp.

The move, which was roundly opposed by the thrift industry and small banks, is seen by some observers as a step toward the creation of a nationwide banking system ultimately dominated by a few large banks. Thomas Pfeiler, assistant general counsel for the U.S. League of Savings Associations, warned recently that the decision would set in motion the "demise of the savings and loan industry."

The California Savings and Loan League called the decision "untimely, unfair and unwise," and held out the possibility of legal action against the Fed. The league contended that a California institution should have been chosen to acquire Fidelity.

The Federal Home Loan Bank Board approved the acquisition last month on the grounds that Citicorp's bid was $143 million better than that of its nearest California competitor.

Californians asserted the issue was too important to be left to regulators and should have been decided by the Congress. The legislators now are putting the final touches on bills governing such takeovers. These would create a priority system under which a takeover is sought first with a like institution in the same state, and only as a last resort, a different, out-of-state partner.

In a 33-page statement accompanying the ruling, the Fed indicated it believed it had complied with the procedures outlined in the bills. The Fed said Citicorp's presence would not have any anticompetitive effects, as the Californians charged, but would increase competition and customer convenience.

Nevertheless, the Fed governors set seven strict conditions aimed at minimizing any unfairness on the part of the $120 billion bank holding company.

Fidelity -- whose name ultimately will be changed to reflect its Citicorp parentage -- will continue to operate as a separate savings and loan. The two institutions will be prohibited from soliciting deposits or loans for each other.

In addition, Citicorp has agreed not to engage in transactions such as the sale of assets with its $2.9 billion subsidiary unless it gets prior approval of the Fed. However this would not bar Citicorp, which has pledged to put $80 million into Fidelity, from making infusions of capital or collecting dividends from the S&L.

Federal regulators seized Fidelity last April because they feared it would become insolvent after suffering an operating loss of $57 million the previous year.

At the time Fidelity was losing about $5 million a month, but it had remaining reserves or net worth of $20 million. Since then, according to the Fed, Fidelity has been experiencing operating losses of $200,000 a day and has now exhausted its net worth. Moreover, depositors have been withdrawing their funds at a rate in excess of $1 million per day.

Citicorp announced that Betty Sue Peabody will become president and chief executive officer of Fidelity, the 42nd-largest S&L in the country. Her previous experience was with Citicorp's retail banking division in upstate New York.

Fidelity has 81 offices in California. Citicorp, which has 853 offices around the country, has 38 offices in that state for commercial lending, leasing and research operations.