Allah says in (2:185)
The month of Ramadhan [is that] in which was revealed the Qur'an, a guidance for the people and clear proofs of guidance and criterion. So whoever sights [the new moon of] the month, let him fast it; and whoever is ill or on a journey - then an equal number of other days. Allah intends for you ease and does not intend for you hardship and [wants] for you to complete the period and to glorify Allah for that [to] which He has guided you; and perhaps you will be grateful.
The bold sentence in the verse might be interpreted as follows (doesn't sound like ease to me, but who knows):
So whoever sights [the new moon of] the month, let him fast it; and whoever is ill (at the time of sighting it) or on a journey (when the new moon was sighted) - then -fasting- an equal number of other days is permissible to him.
Is there any authority held the opinion that only a person who was on a journey when the new moon of Ramadan was sighted has the permission not to fast during that month, while a person who started travelling during the month has not this permission?