Hey Aleksandr Krivonosov, how are you? I hope you are doing just fine!
I clearly understand what you are trying to ask here. I should be very pleased to enlighten you upon the construction of such a sentence.
Firstly, you should know that the word ''So'' can be used in several different ways. However, when the situation entails the veracity and equality of facts about two people or things, you can use ''so'' to convey such a meaning. In this case, you should put ''so'' at the beginning of a clause, followed by 'be', 'have', 'an auxiliary verb', or 'a modal', and then the subject of the clause.
Below you shall find a set of useful examples;
E.g.: ''His shoes are brightly polished; so is his briefcase.''
E.g.: ''She laughed, and so did I.''
E.g.: ''You look upset.'' – ''So would you if you'd done as badly as I have.''
E.g.: ''My friend is addicted to videogames, and so am I.''
As regards your example, we could say ''He is happy, and so am I'', which would be the same as saying ''He is happy. I am too/as well.'' In both cases, you are claiming that something that has just been said about one person or thing is true about another. However, you must invert the order of the sentence should you want to use ''so'' rather than ''too'' or ''as well''.
I hope I have helped you somehow.
Should you have any further questions concerning English grammar, do not hesitate to contact me. I shall be pleased to help.