I don't see any advantage in following this convention. In C, where boolean types don't exist, it's useful to write
if (5 == variable)
rather than
if (variable == 5)
because if you forget one of the eaqual sign, you end up with
if (variable = 5)
which assigns 5 to variable and always evaluate to true. But in Java, a boolean is a boolean. And with !=, there is no reason at all.
One good advice, though, is to write
if (CONSTANT.equals(myString))
rather than
if (myString.equals(CONSTANT))
because it helps avoiding NullPointerExceptions.
My advice would be to ask for a justification of the rule. If there's none, why follow it? It doesn't help readability.