How to append something at the end of a certain line of the text

I want to append something at the end of a certain line(have some given character). For example, the text is:

Line1:  I just want to make clear of the problem
Line2:  Thanks to all who look into my problem
Line3:  How to solve the problem?
Line4:  Thanks to all.

Then I want to add "Please help me" at the end of

Line2:  Thanks to all who look into my problem

And "Line2" is the key word. (that is I have to append something by grep this line by key word).

So the text after the script should be:

Line1:  I just want to make clear of the problem
Line2:  Thanks to all who look into my problem Please help me
Line3:  How to solve the problem?
Line4:  Thanks to all.

I know sed can append something to certain line but, if I use sed '/Line2/a\Please help me', it will insert a new line after the line. That is not what I want. I want it to append to the current line.

Could anybody help me with this?

Thanks a lot!