Restoring Job failed with error 'Could not find a log backup file that could be applied' on Log Shipping in SQL Server (Secondary)?
FULL backups do not break log shipping.  FULL backups simply reset your differential base for all subsequent DIFF backups until the next FULL occurs.

Log shipping occurs in 3 phases:

1- Log backup on the primary

2- Copy log file to destination server (or network share)

3- Restore Log to secondary

If using default settings, these each occur in 15 minute intervals.  This means that it can take up to 45 minutes for a log file taken on the primary to be successfully applied to the secondary.

An easy way to verify that things are in sync is use the 'Transaction Log Shipping Status Report' on the secondary server by right clicking the server name in SSMS and navigating to the following:



EDIT: Here's where to look: