In answer to your question, I would suggest doing what I have done in the past for dry pets, which I have lost. Mainly Siberian and Samoyed Huskies. Please let me elaborate on this.
In the past 11 years, I have bread, raised, trained, and raced over 20 sled dogs. During those 10 years I have lost 3 dogs do to unforseen deaths by wild animals which were encountered during long distance races in the U.S. and through their ongoing training close to home.
What I have done, is I always take photographs of my Huskies during their lives to keep a record of their physical appearance, should one get loose, lost and can't be found, then I have several photo's, in addition to micro-chiping for identification, purposes and proof of ownership.
When one of the dogs have died, I have it cremated, the ashes put into a quality made cremation box. On the box a hand carved or engraved name plate is attached to the box. The box is then placed on a shelf with their last photo taken of them, placed in a frame and either mounted on a wall above their cremation box, or the photo sit on the shelf next to the cremation box.
Now with a Monster Fish which I had become deeply attached to, the same thing could be done, cremation, remains put in a cremation box, placed on a shelf with a photo.
Another option is to take it to a taxidermist, have the fish mounted, the rest of the remains cremated, placed in a cremation box, set on a shelf with the mounted fish attached to the wall above the cremation box or have the fish mounted on a base styled mount, so the fish could be set next to the cremation box on the shelf.
Granted most people will not go to this extreme of imortalization or remembrance of a Monster Fish, but it's no worse than someone having a canine or feline imortalized thru the process of mummification and then displaying it in their house.
Now remember these are only suggestions. If these suggestions are not a financially do-able investment, then I would suggest making a special place for it, so it may be burried with maybe a headstone of some type.