Is it permissible to transfer the remains of a deceased mother, 23 years after her death, to another grave, given that the current grave is built of mud bricks and is susceptible to collapse due to rain?

It is not permissible to exhume a grave without a legitimate Shar'i reason. However, if it suffers damage, such as from a flood or dampness from water, then it is permissible to exhume it and move the deceased to another location. This is supported by what is authentically reported from Jabir ibn Abdullah (may Allah be pleased with them both) that he exhumed his father six months after his burial. And it is mentioned that Talhah ibn Ubaydullah (may Allah be pleased with him) exhumed a fresh body after thirty years due to complaints about seepage (water seeping from the ground). Based on this, if your mother's grave is being damaged by rain or similar factors, it is permissible to exhume it, remove her, and bury her in another place.