"How do I motivate my daughter to make an effort in her language studies?"
How do we motivate any child? SUCCESS!
Your child needs to feel that the effort in writing her letters and phrases is bringing her success and satisfaction. Break down activities into small manageable chunks. Set up a list of what she has to do and also on the list put what she wants to do. Divide them up and let her do a little of both.
Example: If you write 10 of these letters you can have 10 minutes on the Internet. Keep work samples and show her how she has improved from when she first started writing till now so she can "feel and see" her success and growth.