for + noun/pronoun + infinitive

Question

Given

The aim is that we should learn English in six months.

I need to use for + noun/pronoun + infinitive to rewrite it, but I couldn't do it.

My attempts were

1. The aim for us is to learn English in six months
2. For us to learn English is we should in six months.

but I'm not using should in the first one and I don't know if my second attempt is correct.

Answer 1

1. The aim is and English in six months can be held constant in both versions.

2. Then it's simply a matter of transforming

   that Subject^{subject case}(=we) learn^{'subjunctive'}(=should learn)
   into
    for Subject^{object case}(=us)    learn^infinitive(=to learn)

This yields:

The aim is for us to learn English in six months.

Answer 2

EDITED: "The aim is for us to learn English in six months" is clear and correct. [Aside: that is an unrealistic expectation of your students; English can be quite difficult, even for native speakers.]

"For us to learn English is we should in six months" is ungrammatical, just as as you suspected. "Should" implies an expectation, which as I said above, is unrealistic. Posed as a question, the answer might be, "Is it realistic to expect us to learn English in six months?"