I have cycled quite a few tanks by sharing media. Do not take so much that the established tank has any problems.
I have taken as much as 25% of the media from the filter of an established tank. Remember that there are bacteria on all the surfaces in the tank as well as the filter, so that 25% of the filter media might really only be about 1/8 of the bacteria population. That seems to work out OK. The remaining bacteria catch up really quick.