The trick is that aminopterin blocks DNA de novo synthesis, which is absolutely required for cell division to proceed, but hypoxanthine and thymidine provide cells with the raw material to evade the blockage (the "salvage pathway"), provided that they have the right enzymes, which means having functioning copies of the genes that encode them.
Without the THF required to convert dUMP, there can be no TTP, and DNA synthesis cannot proceed, unless TMP can be produced from another source.
The synthesis of IMP, (precursor to GMP and GTP, and to AMP and ATP) also requires THF, and also can be bypassed.
In this case hypoxanthine-guanine phosphoribosyltransferase (HGPRT) reacts hypoxanthine absorbed from the medium with PRPP, liberating pyrophosphate, to produce IMP by a salvage pathway.
The production of monoclonal antibodies was first invented by César Milstein and Georges J. F. Köhler, which earned them the 1984 Nobel Prize in Physiology or Medicine, shared with Niels Kaj Jerne.