Right you had a question. Congratulations for attracting the interest of a foreign publisher. Before you respond, confirm that you're the person who controls these rights. If you signed a book publishing deal, check your agreement to make sure that you, not the publisher, retain certain rights like the right to sell in the foreign territory and the right to make translations. Those are separate rights.
What about your co-author(s)? If co-authors retain the rights then any co-author can make a deal provided that the person making the deal accounts to the co-authors for their fair share. How much is that? In the absence of a co-authorship agreement that spells out percentages, the split is presumed to be pro rata (for example, three ways for three authors). It's always better to get everyone on board before signing and it's even better to have all of the co-authors sign the foreign deal if possible.
What should the deal say? Typically, you grant the foreign publisher the right to make a translation and to publish and sell within a geographic territory. The second part -- the geographical restriction -- is often not that important because most foreign translations have a limited audience (for example it may prove difficult to sell German copies outside of Germany). With this type of deal you can receive royalties for sales or a lump sum and allow the publisher to do a limited print run. (We recommend the limited run with lump sum because it guarantees you a payment.) If additional print runs are expected you can negotiate the value of these and add them in to the contract. Foreign deals are always tough to monitor and therefore, it's relatively impossible to guarantee the publisher is doing the right thing. Again, that's another reason to get a reasonable upfront lump sum payment.