Hello Hadi Soroosh 

You seem to have a couple of problems here.  Note that the Persian (Iran) is not set in your settings, it's not specified.  Sometimes making sure you select the right language so it is set will resolve a problem like this.  However, in your case your termbase viewer seems to be showing both languages under the English so I think you have a different problem.

How did you create this termbase?

Thank you for your response Paul. As you can see in the screenshot below, there's no other option available to specify the language:

I was instructored last week by one of the experienced staff of the church translation office in Stockholm, Sweden. I'm not sure if I remember it completely how the termbase was added, but as far as I remember, we did it through the Termbase wizard.

I actually just tried to add a new Termbase (Test) and interestingly the option for Persian (Iran) is now added to the list. Anyway, by setting that, I do not see any difference in how AutoSuggest functions. 

Anyway, by setting that, I do not see any difference in how AutoSuggest functions.

This might be helpful to see the following shot. The Autosuggest works only when the word exists in a separate segment:

Hi Hadi Soroosh

What you're showing in your last screenshot is AutoSuggest hits from fragment matches, which is different from your termbase. As Paul explained earlier, your Termbase Viewer is showing that you have both terms under English, and so that won't work for term recognition or insertion via AutoSuggest. What you need is to make sure that your termbase is set up with your source and target languages, and that your terms are entered under the appropriate language. Here's a screenshot from my system, where you can see English and Spanish in the Termbase Viewer, and the term being properly recognized in the Term Recognition window and offered in the list of AutoSuggest hits.