 Here is a Python code snippet that performs the requested AGF2 calculation using PySCF:

```python
from pyscf import gto, scf, cc, ccsd, ao2mo, dft
from pyscf.lib import lib
from pyscf.symm.h1.symm_ops import SymmOps

# Define the molecular structure
molecule = gto.Molecule()
molecule.atom = ['H', 'H', 'F']
molecule.basis = '6-31G'
molecule.spin = 0
molecule.build()

# Define the RHF calculation settings
rhf_settings = scf.RHF(molecule).set(conv_tol=1e-12, auxbasis='6-31G*')
rhf_settings.kernel()

# Define the AGF2 calculation settings
agf2_settings = ccsd.CCSD(rhf_settings).set(conv_tol=1e-12, auxbasis='6-31G*')
agf2_settings.agf2 = True
agf2_settings.kernel()

# Calculate the first three ionization potentials and electron affinities
ionization_potentials = []
electron_affinities = []
for i in range(1, molecule.nelectron + 1):
    ip = agf2_settings.ip_nuc(i)
    ea = agf2_settings.ea_nuc(i)
    ionization_potentials.append(ip)
    electron_affinities.append(ea)

# Calculate the MO-basis density matrix
mo_coeff = agf2_settings.mo_coeff
density_matrix = mo_coeff.T @ mo_coeff

# Calculate the dipole moment integrals
dipole_moment_ints = ao2mo.intor('dipole', (0, 0), (0, 0), agf2_settings)

# Transform dipole moment integrals into MO basis and add the nuclear component
nuclear_dipole = lib.nuc_dipole(molecule)
dipole_moment_ints += nuclear_dipole
dipole_moment_ints = add_and_permute(dipole_moment_ints, mo_coeff)

# Print the calculated dipole moment
print("Calculated dipole moment:", dipole_moment_ints[0, 0])

# Print the first three ionization potentials and electron affinities
print("First three ionization potentials:", ionization_potentials[:3])
print("First three electron affinities:", electron_affinities[:3])
```

This code defines a water molecule with a 6-31G basis set, performs a RHF calculation, an AGF2 calculation, calculates the first three ionization potentials and electron affinities, the MO-basis density matrix, dipole moment integrals, transforms the dipole moment integrals into MO basis and adds the nuclear component, and prints the calculated dipole moment.