XBee firmware for BeeStack is required

From XBee/XBee-PRO Series 1 ZigBee Module Firmware Revision History and How to setup Beekit for Xbee Series 1 I understood that it can be possible to implement BeeStack on XBee S1 module.
How can I do it? Is there firmware for this?

What you are asking is actually considered writing your own custom application for the XBee module. It is something that while you are allowed to do this, you are completely on your own. That is to say, Digi is not able to assist you in this endeavor.

It is clear, but I was looking at least for some ready solution just to prove the concept of compatibility. I am not going implement full stack by myself.

If you are not wanting to implement your own code, then you are going to want to look at the S2C ZB modules instead of the 802.15.4 module you are looking at now. Just understand that that the S2C or ZB module as it is called is based off of an Ember chip set and related firmware instead of the Freescale BStack. This is done as the processor on the 802.15.4 module is simply too small to allow one to write an application that does much more than sends and receives data as a router. This is why Maxstream and now Digi never released a full Zigbee application out of beta for the 802.15.4 module. This is also why the XBee ZB (S2) module was developed.

Does it mean that I need to use Ember tools to develop FW for XBee S2C?

Only if you want to develop your own firmware. The firmware that Digi already offers for the module performs all standard radio functions for a Zigbee network including establishing a network, routing data, sending data to and from parent and end devices and much more. I would strongly suggest reading over the product manual for the XBee ZB SMT and new TH modules before you consider going down the Code development path. I think you will find that everything you need is already in it and much moreā€¦