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In your code you define x and y and then redefine then, which may be confusing. Below I distinguish the two definitions and convert g into h by simply evaluating it at new variables:

F = GF(3).algebraic_closure()
Rxy.<x, y> = PolynomialRing(F, 2)
g = x*y
Rx.<xx> = PolynomialRing(F)
Fx = FractionField(Rx)
FxRy.<yy> = PolynomialRing(Fx)
h = g(xx,yy)

In your code you define x and y and then redefine then, re-define them in a new way, which may be confusing. Below I distinguish the two definitions and convert g into h by simply evaluating it at new variables:

F = GF(3).algebraic_closure()
Rxy.<x, y> = PolynomialRing(F, 2)
g = x*y
Rx.<xx> = PolynomialRing(F)
Fx = FractionField(Rx)
FxRy.<yy> = PolynomialRing(Fx)
h = g(xx,yy)

In your code you define x and y and then re-define them in a new way, which may be confusing. Below I distinguish the two variables definitions and convert g into h by simply evaluating it at new variables:

F = GF(3).algebraic_closure()
Rxy.<x, y> = PolynomialRing(F, 2)
g = x*y
Rx.<xx> = PolynomialRing(F)
Fx = FractionField(Rx)
FxRy.<yy> = PolynomialRing(Fx)
h = g(xx,yy)