Panel 2SLS with cross-section fixed effects and without

[reading]

Dear All,
I have a puzzling case here.
I have estimated a panel regression using 2SLS.
There is only one regressor on the right-hand side that changes across cross-sections.
There are three more regressors which only vary over time.

I have stimated this 2SLS panel first using cross-sectional fixed effects, then removing them (no fixed effects at all).
The coefficents estimated with cross-sectional fixed effects and then without are exactly the same for all regressors.

I checked so many times.

Do you think there may be a bug or something is missed from my side?

Many thanks for the help!
Miriam