Undue influence on a testator is difficult to prove but not impossible, according to the Wills, Trusts & Estates Prof Blog in "Corpus Christi Court Upholds Undue Influence Verdict."
A will is assumed valid, if all legal formalities are met, including the will having been signed by the deceased, witnessed and notarized.
This is necessary because there is no way for a judge to ask a deceased person if the will presented in court accurately describes how they wanted to distribute their estate.
Overcoming that assumption of validity, can be very difficult to do.
In most cases, it requires proving that someone pressured (unduly influenced in legal jargon) the testator into making a will in his or her favor.
The article discusses one particular case, where a Texas jury found undue influence.
That verdict was upheld by the court. While the details of the case are not necessarily important, what is important is that undue influence does not necessarily require definitive proof.
In fact, circumstantial evidence can support a finding of it.
Reference: Wills, Trusts & Estates Prof Blog (August 11, 2017) "Corpus Christi Court Upholds Undue Influence Verdict."