AutoFixture: Using GreedyConstructorQuery and still set public properties?

Question

If I configure AutoFixture to choose constructor greedy, properties with public setters are not set. Is it possible to use GreedyConstructorQuery and still have public properties being set automatically?

Example of test that fails. If we remove the customization the test succeeds.

using AutoFixture;
using AutoFixture.Kernel;
using Xunit;

namespace ConsoleAppTests;

public class AutoFixtureCustomizationTests
{
    [Fact]
    public void TestCustomization()
    {
        var fixture = new Fixture();

        fixture.Customizations.Add(
            new MethodInvoker(
                new GreedyConstructorQuery()));

        var test1 = fixture.Create<Test1>();

        Assert.NotNull(test1.Prop2);
    }
}

public class Test1
{
    public Test1()
    {
    }

    public Test1(int? prop1)
    {
        Prop1 = prop1;
    }

    public int? Prop1 { get; set; }
    public int? Prop2 { get; set; }
}

I tried the following:

• Googling the problem without finding anything useful.
• Looking through all built-in ISpecimenBuilders in AutoFixture see if there were anything that could be used. I found one called AutoPropertiesTarget which I tried (fixture.Customizations.Add(new AutoPropertiesTarget(fixture));). It didn't work.