I just purchased new tyres 2.60" and could not find inner tubes bigger enough. Only could find for 2.40". Is it possible use these inner tubes?

Yes.

Agree with Jeff. The usual worst case is a slightly faster leak down over the days/weeks after inflating. It you ride with too low an air pressure the tire can creep/shift around the rim and the tubs valve being trapped by the rim hole will stay put and the tube will get stretched on one side and might bunch up on the valve's other side. But this happens due to too little pressure and not tube fit. So just keep the air pressure topped off before riding. Andy

BTW running a slightly undersized tube has been a BMX racing trick for many decades. Andy

On a smaller tire I'd agree wholeheartedly. But what about the fatness of the tire? I've seen some stupid-low recommendations for tire pressure with wider tires. I don't know where the inflection point would be between "no problem" and "the pressure of a XX tire is too low to keep the tube in place." Do you have any information on how wide a tire or how low tire pressure can go before one runs into the problems you described?

2.60" is roughly about the same as 65mm so if you look at the ISO sizing probably also listed on your tire you can do a search for that size as well. Great article on sizing here. Tire Sizing Systems (sheldonbrown.com) A little long but not necessary to read the entire article. And would agree a 2.40" tube will be fine as well.

Good question and one I have no specific answer for. I do agree that the fat tire riders I know haven't had tire creep issues at their sub 10psi pressures some run at. I suspect there's not one inflection point (nice term, I'll have to remember that to make me sound smarter than I am) and both tire and rim shape subtly comes into play. Andy (who dislikes the wide "Q" of fat bikes and thus won't do more than test ride one after servicing it)

Buy 2.4 tubes for spares. The 2.6 are huge and take up lots of volume.

Tubes usually come in a size that fits a range of several tire sizes. At least they do for the smaller road bike tires I'm use to.

Is there more writing on the box that might give us more information about them? ABC inc. inner tubes might be different than XYZ inc. inner tubes.

The tubes do exist couldn't point you towards them because we don't know what size you need. However you can always go to the shop you purchased the tires from and they will have the tubes or can get them if for some reason they don't carry tubes for the tires.

Yes sometimes running a smaller tube is fine but I would rather have the correct size. The only reason to run the wrong size tube is in an emergency situation or if you are running Tannus inserts.