Legal opinion

As per your concern let me inform you that the situation you've laid down is one of the most common issue that co-owners usually face. Usually, in property matters (joint property) it is often observed that due to greed many times co-owners give rise to unnecessary litigation processes.
This is because many time one owner has sole possession of the property but refuses to pay rent or otherwise compensate the owner who is not in possession; owner refuses to pay his or her share of the property expenses; owners disagree regarding management issues; or even where the co-owners can’t agree about how to handle the property in the future etc.

Basically, in case of absence of an agreement to the contrary there are certain things that the co-owners must remember, such as:-
1.) Co-owners have equal rights to possession of the property, and equal rights and responsibilities. If one co-owner excludes the other from the property, the excluded co-owner can recover the property’s rental value from the excluding co-owner.

2.) If one owner can’t or won’t pay property expenses, the other owner may pay the property expenses to preserve the investment. A co-owner who pays more than his share of operating and maintenance expenses is entitled to a lien against the other co-owner’s interest in the property and/or a greater portion of the proceeds from sale following a partition action.

3.) If a co-owner has paid to improve the property without the consent of the other owner, the co-owner is not entitled to reimbursement.

However, in case the parties cannot resolve their dispute, the parties can apply to a court to determine the parties’ rights and obligations by filing for a partition suit in a civil court of law, that has competent jurisdiction over the property.

In simple terms, a partition suit is a legal method through which a co-owner requests before a court of law to divide the property or its sale proceeds.
There are two different types of division or partitions:-
1.) Physically dividing the property between the co-owners, &
2.) Ordering the property sold (either by private sale or public auction) and the proceeds split between the co-owners.

Henceforth, Mr. B must engage a local prudent civil lawyer and file for a partition suit in a court of law. Meanwhile, he must continue paying the loan installments in order to keep the credit going (do act upon this as per personal lawyers guidance), basically the payments made by Mr. B won't go in vain at any cost because the court will consider his efforts of paying an amount more than his share in the property, through which the court will either order Mr. A to compensate the same to Mr. B with interest or the court can also provide Mr. B for a bigger share in the property as compared to Mr. B taking a note on his efforts for continuing to pay the installments.
Though, the court can give its order based upon its own discretion it will be beneficial for Mr. B in any way, either he'll get a bigger share or he'll get the extra money he paid back from Mr. A along with an interest on the same.


Hope It Helps!


Regards,
Kevin M. Paul