i would still cover the intake of your filter with something, like a sponge or fine netting, so that the babies don't go into the filter, possibly clogging the impeller and causing problems with the filter. it is not the output flow of the filter i'm talking about here, but the possibility of snails going into the filter via the intake tube. i ran an aquaclear 20 on my first 10 gallon snail tank and ended up with lots of babies in the filter because i didn't cover the intake tube.
i would give the babies a little while between hatching and giving them to your friend, to give them a little bit of time to grow and develop. moving them right after hatching would cause a lot of casualties, IMO. give them a week or two, perhaps.
even though you are not keeping any of the babies, it is still a good idea to get a bigger tank for the adult snails and the betta. 5 gallons is not big enough for that bioload.
the 'embryo thingy' or what i call the husk, can be removed and thrown away after the babies hatch out. you may want to freeze it first to make sure any straggling babies do not hatch out in the garbage. i don't crumble mine in the tank or anything, since there are enough snail babies to worry about and making sure i get the last few stragglers is not a concern for me.