Can he work as a typist in a law office that defends criminals?

Praise be to Allah.

Working in the field of law may be permissible or it may be haraam, depending on the situation. If the lawyers support those who have been wronged and strive to have their rights restored, then it is permissible, and even mustahabb. But if it is to support falsehood and help in wrongdoing, and is based on telling lies and giving false witness, then it is haraam. See also question no. 9496. 

The ruling on working in law offices, whether typing or anything else, is to be based on the principle stated above, because typing is something the lawyers need. If the lawyer’s work is permissible, then the means that help with it are also permissible, and vice versa. Allaah says (interpretation of the meaning): 

“Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear Allaah. Verily, Allaah is Severe in punishment”

[al-Maa'idah 5:2]

If you know that the lawyers are defending criminals, and you are asked to type up their reports, it is not permissible for you to do that, because that is helping in sin and approving of evil. The Prophet (peace and blessings of Allaah be upon him) said: “Whoever among you sees an evil action, let him change it with his hand (by taking action); if he cannot, then with his tongue (by speaking out); and if he cannot, then with his heart (by hating it and feeling it is wrong), and that is the weakest of faith.” Narrated by Muslim (49). 

Defending criminals, covering up for them and supporting them is a transgression against the rights of the ummah, because the spread of crime and the lack of punishment have bad consequences as is obvious, and it is a crime against the victim in cases that have to do with specific individuals. 

Any kind of help to do wrong or commit crime is haraam, whether it is by preparing materials, typing them up, defending them, etc. 

What you have to do is advise these people, and refrain from typing up anything that you know is defending falsehood.  If they respond, all well and good, otherwise look for another job which is free of sin and through which you may earn halaal provision. 

We ask Allaah to guide us and you. 

And Allaah knows best.