The short answer is I don't think so.

Axcess is not compatible with data conversion to Lacerte (or even ProSeries).  My understanding is that Axcess does export data for file transfer and migration (unlike PTO) but the file is probably not in a format Intuit could read or even if it is, there is no mapping to bridge the data over.

Even in the event the previous accountant has access to UltraTax, which supports conversion from Axcess, that conversion is only for proforma from a prior year return, which means data exported from UltraTax after the conversion would not help with what you want to achieve, AFAIK.