How can I enter these notes - one melody distributed between the hands?

Search the handbook for "Cross staff notation"

This is possible, but you need to do some rework.
There are two possibilities:

• You enter all the notes in the bass staff.
• select the last three notes and move them to the soprano staff with Ctrl-Shift-UpArrow. (Handbook: cross staff notation)
• adjust the flags with the beam properties.
• in the soprano line hide the existing whole rest
• reverse some of the stem directions with 'x' if necessary

or (second measure):

• enter all notes in both staves with rests which are missing in your picture
• hide the rests
• adjust the beam properties again
• hide remaining rests

• adjust the stem direction

(Example done with MuS 3.6.2)