In general, you can keep female and male bettas in divided tanks. It is rare to have the experience like Paradise mentioned (and I personally have never heard of them damaging their gills) where they harass the other so badly through the divider that it is damaging to one or both of the fish. Now this is in a tank divided with either a piece of craft mesh or acrylic which are both see through in some ways. I do not advise leaving a female in a "dividing tube" more than a couple of days since it is a cramped space and would most definitely stress the female. If you do not have a cycled tank for your female then you need to either divide the tank that the male is in now or get some used filter media from another tank to help keep the levels safe while you are away. Once you are back then you can start conditioning your pair for 2 weeks and then try to spawn them.
