I have read previous posts on this topic here but wanted some clarification. I want to transfer merit (I am familiar and have great faith and practise with the Therevada tradition, and so am interested in this strand of Buddhism...), to someone who is currently experiencing great difficulties and is not open to buddhism or really anything that can help. If I were to transfer merits, it would have to be done without the person knowing and I was wondering if this would give any benefit to the person. Any advice given to this person directly would definitely be unwelcome.....and I want to help in whatever way possible.
It was once said that...
If you were to go along the north bank of the Ganges giving and sacrificing and encouraging others to do the same, no merit comes of that, and no outcome of merit. --SN42.13
A more effective approach to merit is given in AN5.45:
When a mendicant enters and remains in a limitless immersion of heart while using a robe … alms-food … lodging … bed and chair … medicines and supplies for the sick, the overflowing of merit for the donor is limitless … These are the five kinds of overflowing merit, overflowing goodness. They nurture happiness, and are conducive to heaven, ripening in happiness, and leading to heaven. They lead to what is likable, desirable, agreeable, to welfare and happiness.
Merit flows as gifts are used towards progress along the Noble Eightfold Path.
So you see, the answer you seek is in the way you've phrased your request:
"I want to transfer merit (I am familiar and have great faith and practise with the Therevada tradition, and so am interested in this strand of Buddhism...), to someone who is currently experiencing great difficulties and is not open to buddhism or really anything that can help. If I were to transfer merits,"
You've said "I" three times. You want, you are familiar, you will transfer merits. It is important to note that any action you undertake with regard to the self will generate negative karma and prove fruitless in the end. Ask yourself why you'd like to help this person. Is it selfless? Can it be, if it's something you want?
Next, remember that you cannot control another person's actions, only your reaction to them. Conversely, you cannot ever make another feel a certain way. So thinking that you're able to heal or cure or help someone simply by way of desiring is a fool's errand. Your target's mind is more complex than you can ever imagine. It is also very different than what they choose to project on the surface.
So, you are a) misguided and b) trying to ice skate uphill. Are you an enlightened being, sir? If not, then stop this nonsense right now, and go sit and watch your breath. That will prove a far more fruitful (in the Buddhist sense) endeavor than trying to relate peace from a wrong perspective, for the wrong reasons.