Fe replaces Cl with S, making FeSO4 (s), thus removing a part of inhibitors from the anaerobic metabolism by shifting S into solids. But you need to make sure that FeO dose should exceed from the limit which causes inhibition. 

Ferric Chloride will precipitate the sulphide in the digester that would otherwise form salts with essential trace elements required by the methanogens.  For instance there is a biological need for Selenium, Molybdenum, Cobalt, and Manganese to be present and available in the digester at levels typically below 1mg/l.  High levels of H2S/ sulphide in the digester precipitate these trace elements and cause a loss of enzyme based activity in the bacteria and a reduction in respiration.   Dosing with Ferric chloride produces a positive result for a known cost of chemical reagent and is predictable and therefore widely used in full scale digesters for this purpose.  Odour control in the digestate and corrosion control in a gas engine are useful consequences of this method of improving the respiration rate of the bacteria while removing hydrogen sulphide from the biogas.

Fe(III) is first reduced to Fe(II) and then reacts with H2S precipitating as sulfide, removing high levels of H2S that inhibit both methanogens and SRB.

I agree with the rest of the anwers. Toxicity reduction mediated by H2S reduction..

Fellows, thanks for your inputs! My further question then: 

Anaerobic digester has high (1700-2000 ppm) H2S levels, I am thinking about deficiency of micro/macro trace elements inside the reactor.

Instead of adding expensive additives, I am considering of ashes from CHP power plant burning wheat straw (or wood chips) addition.

Would that help? Would that improve or disturb my AD process and would that reduce H2S levels?

In the first instance, whatever Les Gornall says should be given considerable credence.

Second, as mentioned in an answer to a similar question,the manipulation of pH can be critical in determining whether sulfides found in one's slurry are expressed as H2S or not. This has been known for better than a half century, but for some reason is not often mentioned.

Consider the linked chart, found in various publications, tracing back (as far as I can discover) to "Anaerobic Treatment in Pulp- and Paper Waste Management: A Review" (linked to this web site as shown below),

As regards trace elements, at least some research has found that most substrates have adequate resources (see second link below for abstract), but in any case I do not know of research which shows a relationship between trace mineral supplementation and the production of H2S. Do you?

David William House,

The Complete Biogas Handbook, www.completebiogas.com

Article Anaerobic treatment in pulp- and paper-mill waste management: A review

Article Abundance of trace elements in demonstration biogas plant