May I also welcome you to the Forum, I have gone through the recipients of the Monte Cassino Cross both for Grzyb and Grzybowski, but could not find any Aleksander listed.
I have also checked the list of soldiers of the 3rd Carpathian Rifle Division, where there is a Aleksander Grzybowski listed as a Kanonier (Artilleryman) serving with the 2KPAL (2 Karpacki Pulk Artylerii Lekkiej) 2nd Carpathian Light artillery Regiment.
This Aleksander Grzybowski was born in 1911 and had the Service Number (Also found on His ID Tags) : 1911-118-III.
Rita do you have any documentation belonging to your Father at all, any Legitymacja (Authorization) Cards or His AB64 Service and Pay Book as shown below.
AB64 inside which shows his service number and Polish Resettlement Corps (PRC) Number.
Rita have I got the right person when I say did your Father change his name from Aleksander Grzybowski to Aleksander Alexander, whilst living in Berkshire.
Rita it might be worthwhile contacting the British Ministry of Defence for a copy of Both his Polish and English Service Records, this would clarify everything for you. Unfortunately the M-o-D do charge for this service details can be found on the link below
They now charge £30.00p and you would have to fill in the forms and submit it with a copy of your Fathers Death Certificate.
Rita please let us know how you get on.
Apologies for not being able to help you further with your request.