My father is much better. He'll probably start work again within a week.
Literal
Father [topic-は] much better. One-week [even-も] if-passes again work [object-を] will-begin probably.
よろしい is a formal form of いい ('good/fine'). ~もすれば means 'if even ~ passes' — a conditional about time passing. でしょう expresses probability. Two sentences joined by topic continuity rather than explicit conjunction.