CAN THE Rhodesia conference succeed? Practically speaking, the first requirement is that the Muzorewa government agree to a form of majority rule, including minority safeguards, that democratic people outside Zimbabwe-Rhodesia regard as authentic. The British hosts of the conference are working on a constitution embodying that standard and, by reliable reports, both the blacks and the whites in the Rhodesian delegation are moving, though by different paces, toward accepting it. That puts a difficult burden upon the Patriotic Front, but a fair burden, and one essential for the Front to accept if it is to retain the support of the countries sustaining its struggle. They are being increasingly torn by the war.

The second requirement is that the parties agree on scaling down the war and raising a British flag over the various security units that will watch over the transition. The Muzorewa government suspects that the Patriotic Front is afraid of free elections and wishes to preempt or stifle them, and the Front suspects the government will twist the British flag to maintain its own hold. About all that can be said about this murderously difficult problem now is that everyone understands it well.

The conference is a British project, courtesy of Prime Minister Margaret Thatcher. Yet an American shadow hovers over the table. In the defense authorization bill about to go to a House-Senate conference is a Senate-passed amendment calling for the immediate lifting of economic sanctions against Zimbabwe-Rhodesia. Certainly any government in Salisbury that has accepted an equitable new constitution and made a good-faith effort to work out fair transitional arrangements should be rewarded by the lifting of sanctions-- and by diplomatic recognition, too. But it would not be right for the United States alone to offer the prize even as Britain is still holding the parties' feet to the fire. Any decision the conferees make on lifting sanctions should be contingent on the outcome of the negotiations.

The war is destroying Zimbabwe-Rhodesia. Neither side has the strength to dispatch the other expeditiously. Both sides have the capability to make each other pay at grotesque length. The immediate patrons of both sides-- South Africa and the front-line states-- seem worried enough by the prospect of the war spinning even further out of control to support a solution of the sort the British have in mind. Mrs. Thatcher has the necessary courage and energy, the direct interest and the political incentive to try. This is the last chance.