I'd say the easiest way is not splitting them off from India in 1937. However, I was never entirely clear on why that happened in the first place, so I can't say how to prevent it.
During colonial times, industry and the civil service were dominated by Indians. Rangoon was actually half Indian in the 1930s. This provoked a lot of resentment from the native Burmese, and most nationalist groups were agitating for separation by the mid-20th Century.
By and large, Burmese, Indians, and the British viewed native Burmese and Indians as separate groups. There were some political factions in Burma that favored continuing the union with India - the "Anti-Separationists" - but they wanted autonomy and a right to opt for independence later.
Moreover, many of their supporters wanted to continue the union with the rest of India only because they feared the British would separate them, give India independence, and hold on to Burma. As a result, many wanted to remain part of India until independence.