In Romeo and Juliet, what quote best proves that Friar Lawrence came up with the plan to fake Juliet's death?
In addition, at the end of the play, Friar Lawrence explains how Romeo came to be in Verona, at Juliet's tomb, dead, as well as how Juliet -- who everyone believes already died -- has been stabbed and bled, indicating that she was actually alive when she was entombed. At this point, he tells of when Juliet came "to [him] / And with wild looks bid me devise some mean / To rid her from this second marriage [to Paris], / or in my cell there would she kill herself" (5.3.249-252). He tells how he gave her a "sleeping potion" that made her seem dead (5.3.253). He explains that he felt bound to help her because she would have ended her life if he had refused or advised some other means of returning to her life. He goes on to explain what happened after this, how his letter to Romeo didn't make it, how Romeo slew himself at Juliet's tomb, and that Juliet would not leave the tomb with the Friar. Instead she "did violence on herself" (5.3.273). This entire speech, from line 238 to line 278 outlines Friar Lawrence's role in Romeo and Juliet's relationship, including her staged death.
While my earlier answer details the entire plan, your question asked for one specific quote. If I were to choose only one, it would be lines 96-101 in Act 4, Scene 1:
Take thou this vial, being then in bed, And this distillèd liquor drink thou off, When presently through all thy veins shall run A cold and drowsy humor, for no pulse Shall keep his native progress, but surcease. No warmth, no breath shall testify thou livest.
Here, the Friar lays out the plan that Juliet will drink a concoction that will make her appear dead. This portion of text later goes on to say that she will awaken two days later fully functional and within the tomb of her family. At that point, she will be able to escape with Romeo without the knowledge of her family.
The plan comes together in Act 4, Scene 1. There are two blocks of quotes within that scene that serve to hatch the plan. In the first, which spans from line 70-78, the Friar gives a more general sense of the plan, without going into specifics. Here he says that, if Juliet is willing to kill herself rather than marry Paris, perhaps she would be willing to submit to something that is "like death."
In the next block quote (lines 96-109), the Friar gets far more specific, explaining that Juliet is to drink from the vial that has been provided, and that the contents will make her appear as dead for two days. Thereafter she will wake up and reunite with Romeo.
The first indication that Friar Laurence has a plan is in Act IV, scene 1, when he says "Hold, daughter: I do spy a kind of hope," and then goes on to say if you are willing to kill yourself, you probably would be willing to "undertake [a] thing like death," and "if thou darest, I'll give thee remedy."
When we first meet the friar, Act II, scene 3, he is gathering herbs to make potions.