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You can recover the coefficients as follows:
sage: f3.coefficients(sparse=False)
[(a^2 + 1)*b + a + 1, 1]
sage: c = f3.coefficients(sparse=False)[0]
sage: c.parent()
Univariate Quotient Polynomial Ring in b over Finite Field in a of size 2^3 with modulus b^2 + (a^2 + a + 1)*b + a^2
sage: c.lift().parent()
Univariate Polynomial Ring in b over Finite Field in a of size 2^3
sage: c.lift()
(a^2 + 1)*b + a + 1
sage: c.lift().coefficients(sparse=False)
[a + 1, a^2 + 1]
