You have to copy all desired objects from the figure listed in the figure's "children" property.
Here's a demo that copies all objects from 'fig' (blue, regular figure) to 'uifig' (yellow, uifigure).
You probably only want some of the objects which you can select from fig.Children.
uifig = uifigure('Color',[1 1 .8])
fig = figure('color',[.8 1 1]);
ax = axes(fig);
plot(ax, magic(3))
legend(ax)
colorbar(ax)
copyobj(fig.Children, uifig)
