You can put a carbon filter anywhere in your system as long as it does not impede the flow of water through it.
Some floss filtration too may help remove dead particulate flowing out from your new LR.
Even tho LR is technically not cycling like DeadCuring rock..
There is a bit of cycle time beacuse of the new water its in, the slight difference in chemistry from the water where you got your LR from.
It still has some cycling to do. Give it a while.
Just a suggestion..