Grammatical error in the following

Solution 1:

The problem with your phrasing is that it implies that the person you are addressing, rather than yourself, needs to proceed properly with the work. If you had a sign on your door saying

To gain access to the office, press the buzzer and wait to be admitted

you would not take that as meaning that somebody else needs to press the buzzer to let you in.

(And thank you for posting here, rather than leaving it to be thrashed out in the comments.)

Solution 2:

To properly proceed with the work, please send me information for all of the following.

The verb send is part of an imperative construction and uses the plain form of the verb without an expressed Subject. However, there is still an unexpressed Subject that we can reconstruct: it is you, in other words the people being addressed by the speaker.

When we use an infinitive of purpose as an Adjunct in the clause structure, like the one in the Original Poster's example, we do not have to reiterate the Subject if it is the same as the Subject of the main clause:

• To annoy the crocodile, the chicken crossed the road.

Here because the chicken is the Subject of the main clause, we do not need to expressly stipulate the Subject of the infinitival clause. Indeed to do so would be rather odd:

• ?For the chicken to annoy the crocodile, the chicken crossed the road
• ?In order for the chicken to annoy the crocodile, the chicken crossed the road.

Because the speaker intends the Subject of the infinitival clause to be himself, he needs to stipulate the Subject. This is because it is not the same Subject as the unexpressed Subject of the main clause:

• For me to properly proceed with the work, please send me information for all of the following.
• In order for me to properly proceed with the work, please send me information for all of the following.

If we don't stipulate the Subject of the infinitival clause, the natural reading is that the Subject of proceed with the work is the same as the notional Subject of send. In other words we are likely to understand it as:

• For you to properly proceed with the work, please (you) send me information for all of the following.
• In order for you to properly proceed with the work, please (you) send me information for all of the following.