  Given a strict Lie 2-algebra, we can integrate it to a strict Lie 2-group by
integrating the corresponding Lie algebra crossed module. On the other hand,
the integration procedure of Getzler and Henriques will also produce a 2-group.
In this paper, we show that these two integration results are Morita
equivalent. As an application, we integrate a non-strict morphism between Lie
algebra crossed modules to a generalized morphism between their corresponding
Lie group crossed modules.
