That is possible.

If you dont add PageTypeID the property will be a dynamic property

otherProp = new PageDefinition();

otherProp.FieldOrder = prop.FieldOrder;

otherProp.Type = new PageDefinitionType(prop.Type.ID, prop.Type.DataType, prop.Type.Name);

otherProp.PageTypeID = page.ID;

otherProp.Tab = prop.Tab;

otherProp.Name = prop.Name;

otherProp.HelpText = prop.HelpText;

otherProp.EditCaption = prop.EditCaption;

otherProp.Searchable = prop.Searchable;

otherProp.Required = prop.Required;

otherProp.LanguageSpecific = prop.LanguageSpecific;

otherProp.LongStringSettings = prop.LongStringSettings;

otherProp.Save();

otherProp.ClearCache();

Cool! Thanks a lot!