Question on replace of Inductor Coil in a FM Transmitter
Actually the inductor in the 2nd schematic is a single core inductor ! Well not really, it is actually a transformer.

The connection to the antenna is part of the inductor. Actually that inductor is a transformer, the primary side has a centertap, the secondary side is connected to that centertap and the other connection goes to the antenna.

It would have been more clear if this symbol was used:



But then without the core !
T1 and T2 connect to top and bottom right, mid-right and bottom left connect to battery voltage, top left is the antenna output.

This is a configuration that is used to connect the differential signal, present at the collecors of T1 and T2, to a single ended antenna.