HPLC purifications are most effective when Morpholinos are conjugated to a relatively big molecule, such as a peptide (say ca. 200 Daltons or larger), or are conjugated with a net-charged moiety and then the conjugate is purified to remove unreacted oligo. If you are adding a relatively small reactive group and subsequently adding the large molecule, it is probably best to do both additions prior to the purification; that way it is easier to separate the unreacted Morpholino and the activated Morpholino from the conjugate of the Morpholino with the large molecule. You will need to select a column and a mobile phase that exploit a physical property difference between the unreacted Morpholino and its conjugate, whether different hydrophobicity, charge, size, etc. .
If you add a cationic peptide, you might want to put the peptide onto the Morpholino and then run the conjugation product over a cation exchange resin. That captures the conjugated oligos and unconjugated peptide and lets other components, including unconjugated oligos, pass through the column. Then you need to come up with some gentle elution conditions that work for your peptide-Morpholino conjugate .
For oligo analysis, you can use reverse-phase HPLC to separate Morpholino species but the resolution is usually not good. By running the oligos in a pH and salt gradient, starting with high pH to deprotonate the G and T bases, you can use an anion-exchange column (e.g. quaternary alkylammonium packing). As the pH drops the oligos protonate and elute. We used to use this for quality-control analysis of Morpholinos before switching to MALDI-TOF. This method isn’t likely to be useful for preparative HPLC, as the pH conditions are harsh at the start and might damage the oligos.
Morpholinos can be dissolved in water, water-alcohol, or water-acetonitrile solutions. Water with up to 50% acetonitrile can be removed from the oligos by lyophilization. Solubility of a Morpholino varies with the sequence of the oligo.
Possible contaminants include oligos missing one or more bases either internally or at the end (n-1 to n-x sequences for an n-base oligo), sequences capped at the 3’-end (perhaps by a base protection group migrating to the terminal morpholine nitrogen), and oligos with one or more bases still bearing a protecting group. Fortunately, such contaminants are small fractions compared to the desired oligo and will have little or no biological activity at the low concentrations present when the oligos are used, demonstrated by the widespread use of Morpholinos for embryo injection without HPLC purification. Some components such as oligos with a 3’-capping group, will be removed when separating unreacted oligo from oligo conjugates by HPLC (capped oligos would not be expected to migrate with the oligo conjugates).
Morpholinos can be detected in biological matrices by hybridization with a base-complementary fluorescent probe followed by HPLC using a fluorescence detector [3,4]. Other options for detection of Morpholinos in biological samples include a similar fluorescence hybridization approach using capillary electrophoresis , employing surface plasmon resonance with a base-complementary nucleic acid capture surface , using flow cytometry-FISH or sandwich hybridization assays  or ELISA [8,9].
 For size-exclusion HPLC, see:
Liu G, Mang'era K, Liu N, Gupta S, Rusckowski M, Hnatowich DJ. Tumor Pretargeting in Mice Using (99m)Tc-Labeled Morpholino, a DNA Analog. J Nucl Med. 2002 Mar;43(3):384-391.
 For cation-exchange column HPLC, see:
Shabanpoor F, Gait MJ. Development of a general methodology for labelling peptide-morpholino oligonucleotide conjugates using alkyne-azide click chemistry. Chem Commun (Camb). 2013 Nov 11;49(87):10260-2. doi: 10.1039/c3cc46067c.
 For HPLC analysis of Morpholinos from a biological matrix, see:
Arora V, Knapp DC, Reddy MT, Weller DD, Iversen PL.. Bioavailability and efficacy of antisense morpholino oligomers targeted to c-myc and cytochrome P-450 3A2 following oral administration in rats. J Pharm Sci. 2002 Apr;91(4):1009-18.
 For HPLC analysis from a biological matrix also see this poster submitted to the AAPS NBC 2016 conference:
Sun R, Tim S, Clegg R, Bravo O, Zhang J, Rutkowski J. HPLC/FL Quantitation Methods of Eteplirsen in Biological Matrices.
 For capillary gel electrophoresis detection of Morpholinos from a biological matrix, see:
Heald AE, Charleston JS, Iversen PL, Warren TK, Saoud JB, Al-Ibrahim M, Wells JW, Warfield KL, Swenson DL, Welch LS, Sazani P, Wong M, Berry D, Kaye EM, Bavari S. AVI-7288 for Marburg Virus in Nonhuman Primates and Humans. New Engl J Med. 2015;373:339-48. doi:10.1056/NEJMoa1410345.
 For surface plasmon resonance detection of Morpholinos from a biological matrix, see:
Boutilier J, Moulton HM. Surface Plasmon Resonance-Based Concentration Determination Assay: Label-Free and Antibody-Free Quantification of Morpholinos. Methods Mol Biol. 2017;1565:251-263. doi: 10.1007/978-1-4939-6817-6_21.
 For flow cytometry-FISH or sandwich hybridization detection of Morpholinos from a biological matrix, see:
Schnell FJ, Crumley SL, Mourich DV, Iversen PL. Development of Novel Bioanalytical Methods to Determine the Effective Concentrations of Phosphorodiamidate Morpholino Oligomers in Tissues and Cells. Biores Open Access. 2013 Feb;2(1):61-6. doi: 10.1089/biores.2012.0276.
 For ELISA-based detection of Morpholinos from a biological matrix, see:
Burki U, Straub V. Ultrasensitive Hybridization-Based ELISA Method for the Determination of Phosphorodiamidate Morpholino Oligonucleotides in Biological samples. Methods Mol Biol. 2017;1565:265-277. doi: 10.1007/978-1-4939-6817-6_22.
 Burki U, Keane J, Blain A, O'Donovan L, Gait MJ, Laval SH, Straub V. Development and Application of an Ultrasensitive Hybridization-Based ELISA Method for the Determination of Peptide-Conjugated Phosphorodiamidate Morpholino Oligonucleotides. Nucleic Acid Ther. 2015 Jul 15. [Epub ahead of print].