My apologies for the delay
I have asked for your phone number to be removed
I am afraid that your son will not be able to remove his partners name from the Tenancy unless she agrees - or he obtains a Court Order.
The problem is that if he did apply to the court it would be more likely that his Partner would be awarded the tenancy - which is the last thing that you son wants.
The reality is that if his partner wants to be housed by the council then she will have to spend some time in temporary accommodation - it is part of the process.
However most Housing Departments run a Deposit guarantee scheme allowing her to rent privately - if she can find a landlord willing to take her on.
It is more likely that she is angling for one of you to step up and be guarantor - do NOT go there
One option is for your son and his partner to go to Family Mediation
To work out the practicalities of ending the relationship since it is clear that she does not wish to do anything other than complain.
He also needs to make his own enquiries about what help is available from the council for rehousing her - I do not think that she has been honest
Please ask if you need further details