I am looking for a very durable transfer paper which wil not fade after many washes for both whites and blacks. Assuming you would recommend the Translution paper. Can you tell why?

Just to find 1 version paper which is suitable for both, white and black, is hard or in my opinion impossible. Translution comes in the 2 versions and is known as THE or one of the best.

Forgot to mention that I am using a laser printer. Is this paper OK for that? I can't find anything on this forum.

Right. I have being testing the Translution paper long before it came available for sale as an application tester and still convinced that this paper has the best transfer coating formulated available on the market today.

Laser printer transfers? I do heard about people who have used the Translution in combination with a laser printer and they claimed they where successful. I cannot confirm this nor deny because I have never tried it out. I do not have laser but sometimes I know that products can do things accidentally well even when it was not designed for the purpose.

The additional paper/coating properties and what makes it unique compared to other papers is that it is designed for 100% cotton or 50-50 blends which is not an easy task for the coating chemical industry.

From origin this paper is designed for dye and pigment inks which may come from any brand ink and/or printer on the market today, desktop or wide format.

Note: As I assume you are in textiles then you know in the traditional textile printing industry they prefer inks that contain a binder what is responsible to bond the colors with the fabric and therefore responsible for the grade of wash and light fastness. Problems in the past such as clogging the print heads are solved by a few ink manufacturers. (carefully, some but not all)

In digital textile printing terms there are only a few brands to consider a perfect water based pigments and most ideal inks to print with onto textile no matter or direct (DTG) or through transfer media. Pigment inks with this binder can be used on almost all kind of substrates without the usual necessary pre-coating of papers and fabrics even onto canvas for reproductions in museum quality it is the best.

An other important property is that pigment based inks dry much faster and can be transferred to the fabric almost directly after printing and you will have almost never the hassle that you see wheel trails on the print during printing. Today's water based pigment inks with binder can score a washable of 4 on a scale of 5 (FabricFast Ultra ink with Basf method used)

Unlike Pigment, Dye based inks are designed solely for paper printing or for media what is prepared, pre-treated for these inks from the manufacturer which is usual a more expensive media. Pre-treating media for dye base is however necessary because of the longer dry time the inks have. You ever may have noticed in some cases and with some media that the inks stay wet on the surface not able to come dry. Pigment based inks are different in this matter.
This means that the ability to bond with the fabric and make it in some way washable has to come solely from the coating of the paper itself and this is different from paper as much as there are brands.

Then the sharpness. If a housewife wants to print something for a birthday or a similar event she will not notice this but for the professional who has to sell the long dry time is indeed a problem and therefore the dye based inks are not recommended for making reproductions or giclée printing e.g. on canvas. The inks lay wet on the surface for sometime and that impact the sharpness. (photographically reproductions on paper that is prepared for that purpose from the manufacturer of course is not a problem)

This should help you in understanding washable problems with some sort of transfer papers/coating out there using dye based inks.
The better the coating the better the results in soft-feel, durability, smell, residue in unprinted areas, color vividness etc. etc.

The above should also explain the impact of the coating when using laser printing methods. There is no laser powder, as far as I know, that has anything in it that bonds colors with the fabrics the coating of the paper again is responsible for that,and then of course also for the light and wash fastness. Using pigmentinks that contain binders can make a big difference and improve the durability in addition to the properties of the paper coating.