The difficulty is, you have been feeding them and they are at least partially dependent on you, especially if she has kittens, she's going to need all the help she can get to feed the kittens. 

It's arguable whether or not you have a moral responsibility to the cats, but you care, which is important and admirable. Just moving and leaving them as is not the best option. They may well survive, but they will continue breeding and the problem of these stray cats is only increasing.

> One pair of undesexed cats can exponentially be responsible for
> 420,000 kittens, over a 7 year period.

[Animal welfare league][1]


Beyond enlisting a rescue organisation, it's something that's going to require a bit of work on your part.



This is an answer based on experience.

Firstly, do your best to locate where the kittens are. Once you've been able to locate the kittens, the mother and male cat can be trapped using a cage, using food. Some rescue organisations may be able to assist with a cage. I am not sure how soon you are moving, but if you can find the kittens, you'll actually be able to trap the kittens also. This will be a piecemeal process of course, you won't catch all the cats together, it will, most likely be one at a time.

My friend's friend fed a local stray and she saw her have one litter and upon having the second litter she decided to intervene. She gradually trapped all the kittens and the mother, using a food and cage trap. She had a room designated for them. The kittens would hiss at people, as that is what the mother taught them to do.

She desexed the mother and kept her and also kept one of the kittens, re-homing the remaining kittens.

We took two of the kittens and still have them four years later.

This is a pic of them with another rescue cat we own. They are the grey boys.

[![enter image description here][2]][2]

If they are feral cats, they'd be better suited to a [trap neuter return][3] (TNR) program, as feral cats can fend for themselves quite well (1).

(1) Evaluation of the effect of a long-term trap-neuter-return and adoption program on a free-roaming cat population, Levy et al.

http://avmajournals.avma.org/doi/abs/10.2460/javma.2003.222.42


  [1]: https://awl.org.au/advice-education/pet-advice/cat-tips-advice/what-difference-between-feral-and-stray-cats
  [2]: https://i.sstatic.net/ctYQF.jpg
  [3]: http://kb.rspca.org.au/What-is-trap-neuter-return-and-is-it-an-appropriate-strategy-for-the-management-of-unowned-cats_462.html