Importing error : Lookup reference could not be found

Hi,

My scenario is as follows:

1) I have Entity A and Entity B.

2) Entity A has a field called "Name_of_user_in_B".

3) Entity B has a field called "My_name".

4) I have a unique record in Entity B which has "John Doe" in its field called "My_name"

5) I'm importing a single record of Entity A with value of "John Doe" in field "Name_of_user_in_B". This field is mapped to Entity B field "My_name".

I get the error: lookup reference could not be found referring to this field, i.e. CRM cannot find matching name (although John Doe is definitely in a record in Entity B.

I've manually checked these fields, there are no leading or trailing spaces or anything. The contents of "Name_of_user_in_B" and "My_name" are same. How could I resolve this error the best way?