Data roaming problem - Android Q&A, Help & Troubleshooting

Hi guys, I’m having some problems with my girlfriend phone and I’d like to ask your opinion about it.
We both have a tariff with three UK which includes sms, calls and data roaming, and we both have a Samsung Galaxy S5: I bought it in Italy (it was new), while she bought hers here in UK and it was a second hand unlocked smartphone.
Now, the problem is that, despite her phone works nicely in UK, every time we go back to Italy her data roaming doesn’t work at all, while the phone calls and the sms work properly
(the option data roaming is of course enabled).
On the other hand, my phone works perfectly both in UK and in Italy, and we also tested her SIM card in my S5, and in that case data roaming works just fine.
Here a list of tests that we did:
My SIM in her phone -> no data roaming
Her SIM in my phone -> everything works fine
change the Network mode mode in all the possibile options -> CDMA, LTE/CDMA, GSM/UMTS, Automatic
Reconfiguration of the APN settings -> they are the same in both our phones, I report them below:
Name: 3
APN: threeDOTcoDOTuk
Proxy: Not set
Port: not set
Username: not set
Password: not set
Server: not set
MMSC: http : // mmsDOTumDOTthreeDOTcoDOTuk : 10021 / mmsc
MMS proxy: mmsDOTthreeDOTcoDOTuk
MMS port: mmsDOTthreeDOTcoDOTuk
MMS port: 8799
MCC: 234
MNC: 20
Authentication type: Not set
APN type: default,supl,mms
APN protocol: IPv4
APN roaming protocol: IPv4
Enable/disable APN: APN enable
Bearer: Unspecified
Mobile virtual network operator type: None
Mobile virtual network operator value: Not set
The only “difference” (if we can call it so) is in Network mode option:
mine is “LTE/3G/2G (auto connect)”
her is “GSM/WCDMA/LTE (auto connect)”
but I don’t think it actually matters.
So, has any of you any idea of what else I can try to fix this annoying problem?
Rooting the phone and putting on another ROM may be of some help?
I have really no idea, so any suggestion is very welcome!
Thank you very much