Based on the situation you have described, isolating the plasmid from the ampicilin-resistant strain of E. coli and allowing it to be taken up by a separate, non-resistance strain of E. coli would be the most efficient, and cost effective method of determining whether or not the AmpR gene is located on the plasmid or the bacterial chromosome itself.
In order to do this, you would need to first grow a culture of the ampicilin resistant strain, from which you could induce lysis of cells in order to obtain a solution containing free plasmids.
Several different plasmid isolation or mini-prep procedures exist that are typically quite effective, if done correctly.
Additionally, many specific "plasmid-isolation" and "plasmid-purification" kits exist that would offer the materials and instructions needed to undergo this process: Isolating your Addgene Plasmid DNA from Bacteria
After properly isolating the plasmid from your ampicilin-resistant strain, you would then need to insert that plasmid into a non-resistant E. coli strain. Bacterial transformation via electroporation is a commonly used technique that causes increased permeability of bacterial cell membranes, enabling the plasmid to enter or be taken up by the cells.
Once these cells have been allowed to "recover" they can then be grown in liquid or solid culture containing ampicilin. Growth would indicate the AmpR gene is present in the bacterial strain, and that the plasmid is responsible for carrying this resistance. Likewise, no growth would suggest that the gene must have be present on the bacterial chromosome instead.