Copying MySQL tables, InnoDB tables not recognized
While .frm, .MYD, .MYI are enough for MyISAM, ibdata1 (InnoDB Global Table space) is needed for InnoDB even if you are using innodb_file_per_table = TRUE.

ibdata1 holds meta data for InnoDB Tables. InnoDB Table can't be found without those meta data. So you are getting "Table 'table_name' doesn't exist". error.

MySQL Manual states that


  You cannot freely move .ibd files between database directories as you can with MyISAM table files. The table definition stored in the InnoDB shared tablespace includes the database name. The transaction IDs and log sequence numbers stored in the tablespace files also differ between databases.


The main reason is Table id is different both source and dest. DB's ibdata1. So ibdata1 should be moved from src to dest.