I was recently terminated from my job. I was given the reason of "restructuring". Although their reason is total bull, since they've already replaced me. I want to ask for a bigger severance package and I'm not sure how to write this request. Any help is appreciated

I can't you write a letter, not knowing anything about you, the company, or the severance package they gave you. I believe that it will be a waste of your time and energy anyway. In this economy, I'd be glad to have received any severance at all.

As for the bull, of course restructuring is often a euphemism for either clearing out people they don't want or getting new people for less money. If you are older and worked there a long time, you might have an age discrimination suit.

Does the company have an established severance policy? If so, they will not change it.

Unless you think you can "blackmail" the company with a wrongful termination suit, don't waste your time.

I had a meeting with a lawyer. He suggested if he was to handle my case he would get me 8 months severence instead of the 4 months I was offered.
The reason I believe(know) my termination was bull is because I've been replaced already with someone who's being trained to do my job. I'm was making average salary not more then really anyone else in my department, possibly less.

I really just want to know what points I need to make when replying to the offer of serverance they've given me.

Of course how much of that 8 month salary will the lawyer get,

But I will have to assume you aer not in the US, can you tell us where you are at, customs there may be different, in the US you would seldom even get 4 months, that is much more than normal

We heard you about the BS the first time.
I don't think you understand the rights of employers to fire.
Layoffs have to follow certain laws in the US, including rules about replacements. Employers CAN fire you, replace you, and not give you any severance at all.
If it falls under civil rights violations (race, gender, age, etc.) you can try a lawsuit.
The lawyer will cost you money up front. What if you don't win? People here are claiming you have little to no chance; maybe the lawyer just needs money.
If the company has published policy about warnings, probation, and other steps before firing, then you might have a case. But you haven't said that they do.
As for just wanting to know what points to make in a letter, I won't waste the time, and we still know too little anyway. I am puzzled that you still think there is some sort of generic template for this demand letter.

First, when posting a follow-up question or info, please use the Answer options at the bottom of the page rather than the Comments.

And what grounds did this lawyer say you could use? I suspect he probably thinks the company will increase your severance because it will be cheaper than fighting a lawsuit.

In the US, most states are "at will" employers. This means they can terminate your employment for no reason whatsoever and are not required to pay severances unless mandated by written company policy. Were other people terminated in this restructuring?

So you were made an offer, does this offer require a response? Was an alternative give? An offer generally involves a choice so was there a choice here or was this letter a statement that you have been terminated and will get x severance? Also you mention nothing about employment reviews Has there been any problems recently?

There is no way we can suggest what you can say without knowing the full picture.