Any class power can be taken by a character if:
- That character can take powers of that class
- The class power in question has an explicit level and the character is eligible to take powers of that level. (Either from a newly gained power, or from retraining)
- The class power is of the same type (attack or utility)
This goes for Essentials characters taking regular powers and vice-versa.
The Slayer (I'm assuming this is what you meant by "Essentials Fighter" gains, at level 1 two stances (out of 6 to chose from). These are all listed as
Fighter Utility powers, so they are not eligible for a regular fighter to take. Compare to the powers gained at second level which are listed at
Fighter Utility 2. Those are eligible for any fighter to take.
The rules for this are on p57 of the Heroes of the Fallen Lands book.