You mentioned in a previous question and answer that while it is sunnah to stop at the end of all or any ayaat of the Blessed Qur'an, it is not forbidden to link them if one wishes; can different surahs be linked as well?

Answer

Yes, one surah can be joined with the next sequential surah in three permissible ways. 

1. Reciting the last aayah of the first surah, stopping and taking a breath, then reciting the basmalah of the next sequential surah, stopping and taking a breath, then reciting the first aayah of the intended surah. The three steps have been therefore been done separately here.

2. Joining the last aayah of the first surah with the basmalah and then the first aayah of the next sequential surah in one breath.  The three steps have been done continually in one breath in this case.

3. Reciting the last aayah of the first surah, stopping and taking a breath, then reciting the basmalah with the first aayah of the next surah in one breath.  There is the separation of the last surah from the basmalah of the next surah, but a continuum of the basmalah with the beginning of next surah, in one breath. 

Please note that when there is a continuum between two steps, the appropriate vowels on the last word of either the first surah, and/or the basmalah need to be used. 

It is NOT allowed to join the end of the first surah with the basmalah, then stop and take a breath, then continue reciting the first aayah of the next surah.  This inaccurate way of joining the two surahs could lead a listener to believe that the basmalah was part of the first surah, not the beginning of the second surah.

Another point to be made is that the linking of one surah to another can only be done with sequential surahs, not with random surahs.