I`m calling a service... and response from this service has a value that I should write back in tax amount. I had even tried to changed the value from Sage Database.. the value has been changed successfully but still only at Tax Details -> Tax Amount they are zero overthere.

An alternate way to do this is to ignore the tax fields. Create a miscellaneous item for /TAX, then add a line with your amount.

I would recommend that you let Sage calculate the taxes. Perhaps you are looking at the wrong problem to solve? I have done integrations with shopping carts and Sage, and the issue has always been to get the Shopping cart to respect the Sage taxes (well not really an issue, but a "problem" in the list to solve).

I would say that if taxes are set up properly in Sage for an invoice, and your service is sending data that has different taxes - there is a disconnect there. Either adjust the sage tax settings so they mirror the data from your service, or adjust the source of the service so that they mirror Sage. Taxes are kind of a known quantity, and you should be able to get a harmonization without putting in the "wrong" taxes into Sage (which it sounds like you are trying to do - at least "wrong" in the sense that Sage isn't set up to calculate in the way you want to do it so it overwrites your changes).

Please be aware, that even if you got your changes and "wrong" taxes set in Sage, someone else could just look at the invoice, and it would revert back to it's "correct" setting, overwriting what you have done. This is a danger sign and you need to stop and think about this.

There is only one tax reality. Probably Sage is set up correctly as it was probably done by accountants. And an external service was probably done by computer scientists. I would guess that the tax reality lies in Sage with the accountants and you have to get your external service to match that reality.