Adding a Far DR secondary server Log shipping on already configured SQL server
The issue is copying a full backup might take more than 12 hours from primary to really far DR and there is 4 schedules of daily full backup on Primary each of 6 hours interval.
... configure the log shipping on the Far DR without any delay ...

These two are competing items. If it takes 12 hours to transfer and you must transfer full backups every time then I don't see how that will fit in a 6 hour window, let alone be able to do anything of use with it.
You'll either need to push back on doing this or ask for better bandwidth.
If, however, you don't have to send the same full backup each time, then a one time full with logs between may be possible depending on the rate of change in the database. Obviously this all depends on what the requirements say.

[comment]...consider using mirroring or AlwaysOn High Availability Groups instead.

Potentially, depending upon the requirements (which we currently don't have or know), although this could lead to other undesirable consequences if the latency is very high. Availability groups do not like latency.