from Higashi-Umeda to Osaka station for Kyoto (rapid line) You may need 10 or more minutes
to walk from subway Higashi-Umeda Station to JR Osaka station.
JR Special Rapid trains bring you
from Osaka Station to Kyoto Station in about 30 minutes,
making stops at Shin-Osaka, Takatsuki and Kyoto Stations in this order.
(Rapid trains, which make more stops, go slower than Special Rapid trains.)
Where is your first destination in Kyoto City?
You alternatively can travel
by subway Tanimachi and Sakaisuji Lines + Hankyu Senri and Kyoto Lines
to Karasuma Station or Kawaramachi Station in Kyoto City
(below the east-west Shijo-dori Street),
making one or two quick transfers.
Disembarking at Karasuma Station,
you can get out through the west ticket gate,
turn to the left,
walk a little to subway Shijo Station
and take a train on the Karasuma Line for a few minutes to Kyoto Station.
http://www.hankyu.co.jp/global/common/pdf/station_guide/karasuma.pdfhttps://www2.city.kyoto.lg.jp/kotsu/tikadia/img/map/sta/pdf/k09map.pdfHigashi-Umeda Station (T20)
http://www.kotsu.city.osaka.lg.jp/station-guide/T/t20/: Departure at Track 2
{ Subway Tanimachi Line }
Arrival at Track 2 (of Tanimachi Line):
(T21) Minamimorimachi Station (K13)
http://www.kotsu.city.osaka.lg.jp/station-guide/K/k13/: Departure at Track 2 (of Sakaisuji Line)
{ Subway Sakaisuji Line
until (K11) Tenjinbashisuji 6-chome
+ Hankyu Senri Line}
Awaji Station
http://www.hankyu.co.jp/global/common/pdf/station_guide/awaji.pdf: Here your two trains are to use
either the same track or the two tracks beside the same platform.
{ Hankyu Kyoto Line}
Karasuma Station | Kawaramachi Station.
At Minamimorimachi Station (Sakaisuji Line's Track 2),
depending on the timing,
you may catch a Semi Express train bound for Kawaramachi,
which makes a stop at Karasuma Station on the way.
Otherwise,
you can take a train
(which is to run beyond Tenjinbashisuji 6-chome)
until Awaji Station,
where you can catch a train bound for Kawaramachi.