Ruling on financial sponsorship; does it make a difference if the debt is transferred from one lender to another?

Firstly: 

If the sponsorship that was given to the company was
sponsorship for a riba-based loan – which is what appears to be the case
from your words, because you say that the bank is “normal”, i.e., riba-based
– then it is haraam sponsorship, and comes under the heading of cooperating
in sin and transgression, and Allaah forbids that in His words
(interpretation of the meaning):

“… but do not help one another in sin and transgression.
And fear Allaah. Verily, Allaah is Severe in punishment…”

[al-Maa’idah 5:2]

What you have to do is repent to Allaah for your action, and
resolve not to repeat any such thing; and you have to advise the person whom
you sponsored to get rid of his loan and haraam financial dealings. You must
also withdraw your sponsorship if possible. 

But if it is legitimate shar’i sponsorship, and the
transaction is not haraam, then your sponsoring of him is permissible;
indeed it is a good action, and you will be rewarded for it, and it comes
under the heading of kind treatment of people. 

Secondly: 

It is well known in companies – and it is not contrary to
sharee’ah – that when a company is sold or amalgamated into another, then
its assets and obligations are transferred to the other company, and
everything that is owed to the first company by others is now due to the
second company, and what the first company owes is now owed by the second. 

Based on this, the new bank is entitled to ask you for the
sponsored money. 

In the case of a riba-based loan, it is not entitled to ask
you for anything more than the capital only, and not the interest, because
the Prophet (peace and blessings of Allaah be upon him) said: “The riba
of Jaahiliyyah is abolished.” Narrated by Muslim (1218). 

Al-Nawawi said in Sharh Muslim: His words (peace
and blessings of Allaah be upon him) concerning riba, “it is all abolished”
refer to the interest on the capital, as Allaah says (interpretation of the
meaning): “but if you repent, you shall have your capital sums”
[al-Baqarah 2:279]. What I have mentioned is clarification, otherwise what
is meant is clear from the words of the hadeeth, because riba is interest,
and if riba is abolished then what it means is that the interest is
abolished, and the meaning of abolishing is rejecting and annulling. End
quote. 

And Allaah knows best.