discharge and transfer of care same day

We have a patient who was discharged from our hospital from inpatient status (99235) and there was basically a transfer of care to another hospital. The other hospital billed an initial inpatient visit (99223) and now our charge is denying because they can't be billed on the same day. (I am billing the professional portion of these charges.)

Do we need to be using something other than a discharge code for a transfer of care?

Thanks

discharge and transfer of care same day