Is it considered forbidden to listen to soft songs once with the intention of memorizing their lyrics and melody, and then singing them to one's husband without musical accompaniment?

A wife singing for her husband is permissible with conditions, but it is not permissible to listen to songs that include musical instruments. This is wrong. The need to memorize a song does not make listening to it with musical instruments permissible. One can find the lyrics of the song written down to memorize them and sing them to the husband.