Commemorating the death of a previous spouse after remarriage:

Should a husband commemorate the Yahrzeit of his deceased wife if he has since remarried [i.e. light a Yartzeit candle, recite Kaddish, visit the Kever, etc]?[1]

It is not proper at all to do so, and thus it should not be done.

Those reciting Yizkor may add in their recitation, the names of other souls and deceased relatives, such as a sibling, or spouse. If a child passed away r”l, his name may also be mentioned, even if he was below the age of Chinuch. If one’s spouse passed away and they then remarried, it is debated whether their names may be mentioned in Yizkor or if they are to have another do so for them.[2]

It is better not to do so, unless it is written in an incospicuous manner, such as on the side of the grave.

This matter is disputed amongst Poskim[5], and hence it is best to establish the Matzeiva prior to the marriage.

May one who remarried visit the Kever of his previous wife or her previous husband?[6]

The custom is for a woman who remarried not to visit the grave of her first husband, and for a man who remarried not to visit the grave of his first wife. Due to this, it is customary for the spouse to visit the grave of their previous spouse prior to remarrying. 

One who is in mourning for his wife, and has since remarried, may not be comforted for her passing inside his home. Outside his home, if he is met outside, one may say “Be comforted” in a soft tone and with a heavy heart. If he did not remarry, he may be comforted until three festivals pass from the time of burial. After 30 days, he is not to be directly comforted for the loss. This means that the comforter is not to mention the name of the deceased to the mourner, but is to simply say “be comforted.” [The custom today however is not to say even “Tisnachem” after the Shloshim.”[8]]

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[1] Shut Chasam Sofer Y.D. 355 regarding Likkut Atzamos; Sefer Zichros Moshe p. 65 in name of Chasam Sofer that he did not allow his wife to light a candle for her previous husbands Yartziet; Beir Moshe 4:104 based on Michaber 385:2 and Moed Katan 21b and Hagahos Maimanis Hilchos Semachos; Nitei Gavriel 70:21; See Dudaei Hasadeh 14; Gesher Hachaim 31:9; Nitei Gavriel Aveilus 79:10; See Nitei Gavriel Vol. 2 11:1-3; Ateres Moshe 2:240; Nitei Gavriel 66:332-33; Minchas Moshe 114 [forbidden]; Seridei Eish 2:136; Nitei Gavriel 80:5-6; See Gesher Hachaim 29:8

[2] See Dudaei Hasadeh 14; Gesher Hachaim 31:9; Nitei Gavriel Aveilus 79:10

[3] See Ateres Moshe 2:240; Nitei Gavriel 66:332-33

[4] See Nitei Gavriel 67:21 in length

[5] See Minchas Moshe 114 [forbidden]; Seridei Eish 2:136 [permitted and obligation]

[6] Nitei Gavriel 80:5-6; See Gesher Hachaim 29:8

[7] Michaber 385:2; Moed Katan 21b; See Nitei Gavriel Vol. 2 11:1-3

[8] Aruch Hashulchan 385:3