You must freeze the projections. Open the Explorer, expand the enveloped object node, go into clusters. There is a node called Texture_Coordinates_AUTO. Expand this, and you'll see your projections. Freeze them and the UVs will stick with the envelope.
You know they are freezed when you can their name followed by a (Explicit_UVW).
Hope this helps
Salutations - Cheers
Bernard Lebel